{"id":4169,"date":"2013-11-25T07:41:49","date_gmt":"2013-11-24T23:41:49","guid":{"rendered":"https:\/\/lttt.blog.ustc.edu.cn\/?p=4169"},"modified":"2013-11-25T07:41:49","modified_gmt":"2013-11-24T23:41:49","slug":"%e6%9c%89%e6%9c%8b%e8%87%aa%e8%bf%9c%e6%96%b9%e6%9d%a5%e4%b8%80%e4%b8%80-%e4%b8%93%e8%ae%bf-mariano-giaquinta-%e6%95%99%e6%8e%88","status":"publish","type":"post","link":"https:\/\/lttt.vanabel.cn\/?p=4169","title":{"rendered":"\u6709\u670b\u81ea\u8fdc\u65b9\u6765 \u2014\u2014 \u4e13\u8bbf Mariano Giaquinta \u6559\u6388"},"content":{"rendered":"

\u7b56 \u753b : \u5218\u592a\u5e73
\n\u8bbf \u8c08 : \u5218\u4e30\u54f2\u3001 \u9648\u6021\u5168
\n\u65f6\u95f4: \u4e2d\u534e\u6c11\u56fd\u4e5d\u5341\u4e00\u5e74\u516b\u6708\u4e5d\u65e5
\n\u5730 \u70b9 : \u4e2d\u7814\u9662\u6570\u5b66\u6240
\n\u6574 \u7406 : \u9648\u6021\u5168
\n\\begin{abstract}Mariano Giaquinta \u662f\u5728\u610f\u5927\u5229\u6df1\u539a\u7684\u53d8\u5206\u5b66\u7684\u4f20\u7edf\u4e0b\u8bad\u7ec3\u51fa\u6765\u7684\u6570\u5b66\u5bb6, \u627f\u7ee7Dini, Fubini, Tonelli, Caccioppoli \u548cDe Giorgi \u7684\u4f20\u7edf, \u5728\u53d8\u5206\u5b66\u7684\u73b0\u4ee3\u7406\u8bba\u548c\u692d\u5706\u578b\u504f\u5fae\u5206\u65b9\u7a0b\u7ec4\u7684\u89e3\u7684\u5b58\u5728\u6027\u53ca\u89e3\u7684\u6b63\u5219\u6027\u95ee\u9898\u4e0a\u90fd\u6709\u91cd\u8981\u7684\u8d21\u732e\u3002\u4ed6\u66fe\u4efb\u6559\u4e8e\u4f5b\u7f57\u4f26\u65af\u5927\u5b66\u3001 \u6bd4\u8428\u5927\u5b66, \u76ee\u524d\u5728\u9ad8\u7b49\u5e08\u8303\u5b66\u6821\u62c5\u4efb\u6559\u6388, \u5e76\u4efbDe Giorge\u6570\u5b66\u7814\u7a76\u4e2d\u5fc3\u4e3b\u4efb\u3002\u610f\u5927\u5229\u9ad8\u7b49\u5e08\u8303\u5b66\u6821\u662f\u7531\u62ff\u7834\u4ed1\u6240\u521b\u7acb, \u662f\u610f\u5927\u5229\u6700\u91cd\u8981\u7684\u79d1\u5b66\u5bb6\u7684\u517b\u6210\u6240, \u8457\u540d\u7684\u7269\u7406\u5b66\u8005Fermi \u5373\u51fa\u751f\u4e8e\u6b64\u3002\\end{abstract}
\n
\n\u5218<\/strong>: \u4eca\u5929\u662f\u4e3a\u4e86\u300c\u6570\u5b66\u4f20\u64ad\u300d \u5b63\u520a\u7684\u300c\u6709\u670b\u81ea\u8fdc\u65b9\u6765\u300d \u4e13\u680f\u800c\u505a\u8fd9\u4e2a\u8bbf\u95ee\u3002\u5f53\u7136\u610f\u5927\u5229\u662f\u591f\u8fdc\u7684!(\u4f17\u7b11)\u4f60\u662f\u4f4d\u8457\u540d\u7684\u6570\u5b66\u5bb6, \u53ef\u5426\u8bf7\u4f60\u5148\u7b80\u5355\u5730\u8c08\u8c08\u4f60\u7684\u6c42\u5b66\u80cc\u666f, \u5982\u679c\u53ef\u80fd\u7684\u8bdd, \u662f\u4ec0\u4e48\u5c06\u4f60\u5e26\u5165\u6570\u5b66\u7684\u9886\u57df?
\nGiaquinta<\/strong>: (\u4ee5\u4e0b\u7b80\u79f0G) \u8fd9\u662f\u4e00\u4e2a\u597d\u95ee\u9898! (\u4f17\u7b11) \u9ad8\u4e2d\u65f6\u4ee3, \u6211\u5bf9\u4e8e\u6570\u5b66\u5e76\u4e0d\u611f\u5230\u7279\u522b\u5730\u56f0\u96be\u3002\u540e\u6765, \u542c\u8bf4\u5728\u6bd4\u8428(Pisa) \u53ef\u4ee5\u5b66\u5230\u597d\u7684\u6570\u5b66, \u6211\u4fbf\u5230\u90a3\u513f\u8bfb\u4e66\u3002\u55ef\u2026 \u6211\u5fc5\u987b\u8bf4\u6211\u4e0d\u662f\u4e00\u4e2a\u597d\u5b66\u751f\u3002\u5f53\u65f6\u6211\u7684\u4e3b\u8981\u76ee\u6807\u662f\u5c3d\u5feb\u5b8c\u6210\u5b66\u4e1a, \u5e76\u5728\u7ecf\u6d4e\u4e0a\u80fd\u591f\u72ec\u7acb\u3002\u83b7\u5f97\u5927\u5b66\u5b66\u4f4d\u4e4b\u540e, \u6211\u6709\u4e00\u6bb5\u7f8e\u597d\u7684\u65f6\u5149, \u56e0\u4e3a\u6211\u88ab\u5927\u5b66\u7559\u4e0b\u6765\u5f00\u59cb\u5728\u6bd4\u8428\u505a\u7814\u7a76\u3002\u90a3\u65f6, \u6bd4\u8428\u771f\u662f\u4e2a\u975e\u5e38\u597d\u7684\u5730\u65b9, \u50cfBombieri, De Giorgi, Stampacchia, Andreotti, Campanato, Prodi \u548cVesentini* \u5168\u90e8\u5728\u90a3\u513f\u3002
\n\u5218<\/strong>: \u90a3\u662f\u4ec0\u4e48\u65f6\u5019?
\nG<\/strong>: \u6211\u662f1966\u52301969\u5c31\u8bfb Pisa \u5927\u5b66\u3002\u7d27\u63a5\u7740\u5f97\u5230\u5b66\u4f4d\u4e4b\u540e, \u6211\u5148\u5728\u5df4\u9ece\u5f85\u4e86\u4e00\u5e74, \u7136\u540e\u56de\u5230\u6bd4\u8428\u76f4\u52301976\u5e74, \u90a3\u5e74\u6211\u5f97\u5230Modena \u7684\u6559\u6388\u804c\u4f4d\u3002\u800c\u540e\u6211\u5728 Ferrara \u5f85\u4e86\u4e24\u5e74, \u7136\u540e\u5230\u4f5b\u7f57\u4f26\u65af\u5927\u5b66(The University of Florence)\u3002\u516d\u5e74\u524d\u5230\u6bd4\u8428\u5927\u5b66, \u4e09\u5e74\u524d\u6211\u5f00\u59cb\u5728\u9ad8\u7b49\u5e08\u8303\u5b66\u6821(Scuola Normale Superiore) \u62c5\u4efb\u6559\u6388\u3002\u6211\u8ba4\u4e3a\u5728\u5fb7\u56fd\u6ce2\u6602\u5927\u5b66(University of Bonn) \u5ea6\u8fc7\u76f8\u5f53\u7684\u65f6\u95f4\u5bf9\u6211\u800c\u8a00\u662f\u6bb5\u5f88\u91cd\u8981\u7684\u7ecf\u5386, \u6211\u5927\u6982\u5728\u5fb7\u56fd\u5f85\u4e86\u4e8c\u3001 \u4e09\u5e74\u7684\u65f6\u95f4, \u5f88\u6709\u6536\u83b7, \u56e0\u4e3a\u6ce2\u6602\u7684\u6570\u5b66\u7814\u7a76\u6240\u603b\u8ba9\u6211\u611f\u53d7\u5230\u4e00\u80a1\u5bf9\u4eba\u6709\u6240\u542f\u53d1\u7684\u6c14\u6c1b\u3002
\n\u5218<\/strong>: \u4f60\u53ef\u5426\u591a\u8bf4\u4e00\u4e9b\u4f60\u5728\u6bd4\u8428\u7684\u90a3\u6bb5\u7f8e\u597d\u7684\u65f6\u5149?
\nG<\/strong>: \u90a3\u771f\u662f\u4e00\u6bb5\u7279\u6b8a\u7684\u65f6\u5149\u3002\u90a3\u65f6De Giorgi \u521a\u521a\u53d1\u5c55\u4e86\u6781\u5c0f\u66f2\u9762(minimal surfaces) \u7684\u7406\u8bba\u548c\u8bc1\u660e\u4e86\u692d\u5706\u65b9\u7a0b(elliptic equations) \u7684regularity theorem; Bombieri, De Giorgi\u548cGiusti \u6b63\u7ed9\u51faBernstein \u95ee\u9898\u7684\u53cd\u4f8b; \u800c\u540c\u65f6Stampacchia \u4e5f\u6b63\u53d1\u5c55\u53d8\u5206\u4e0d\u7b49\u5f0f(variational inequality) \u7684\u7406\u8bba\u3002\u8bb8\u591a\u6709\u610f\u601d\u7684\u6280\u5de7\u90fd\u662f\u5728\u90a3\u65f6\u53d1\u5c55\u7684, \u50cfregularity \u53capartial regularity \u7406\u8bba\u4e2d\u7684\u6280\u5de7, \u53ef\u8bf4\u662f\u8fd1\u5e74\u6765\u53d1\u5c55\u7684\u6240\u6709regularity \u7406\u8bba\u7684\u6a21\u578b\u3002
\n\u5218<\/strong>: \u5f53\u65f6, \u4f60\u662f\u5982\u4f55\u63a5\u89e6\u8fd9\u4e9b\u4f18\u79c0\u7684\u4eba\u5462?
\nG<\/strong>: \u7ecf\u7531\u4e0a\u8bfe\u548c\u53c2\u52a0\u7814\u8ba8\u4f1a; \u8fd8\u6709\u8ddf\u4ed6\u4eec\u4ea4\u8c08\u3002\u6211\u8bb0\u5f97\u90a3\u65f6\u4e0d\u50cf\u73b0\u5728\u6709\u90a3\u4e48\u591a\u7684\u4e66\u7c4d, \u4f46\u662f\u90a3\u513f\u6709\u7740\u4e00\u79cd\u8ba8\u8bba\u8bb2\u8ff0\u7684\u4f20\u7edf\u3002\u8fd9\u79cd\u4f20\u7edf\u662f\u975e\u5e38\u6b63\u9762\u7684, \u56e0\u4e3a\u4eba\u4eec\u80fd\u591f\u76f8\u5f53\u5feb\u5730\u77e5\u9053\u65b0\u7684\u4e8b\u60c5\u3002\u6b64\u5916, \u90a3\u65f6\u5bf9\u4e8e\u53d1\u8868\u8bba\u6587\u7684\u538b\u529b\u662f\u6bd4\u8f83\u5c0f\u7684\u3002\u8fd9\u4e9b\u662f\u5f53\u65f6\u6587\u5316\u7279\u8272\u7684\u4e00\u90e8\u4efd\u3002\u90a3\u65f6\u5728\u6bd4\u8428\u5e76\u6ca1\u6709\u5982\u6b64\u591a\u7684\u6559\u5e08, \u5728\u6570\u5b66\u8fd9\u79d1\u6216\u8bb8\u53ea\u670910\u4f4d, \u4f46\u73b0\u5728\u5927\u7ea6\u670970\u4f4d\u3002\u6240\u4ee5\u8981\u65f6\u65f6\u77e5\u9053\u6216\u8bb8\u6709\u4ec0\u4e48\u4e8b\u60c5\u6b63\u5728\u53d1\u751f\u5c31\u53d8\u5f97\u6781\u5ea6\u56f0\u96be\u3002\u5341\u4e2a\u4eba\u5e38\u5e38\u80fd\u76f8\u4e92\u5bf9\u8bdd, \u4e03\u5341\u4e2a\u4eba\u5c31\u5f88\u96be\u4e86\u3002\u8fd8\u6709,\u5982\u679c\u6709\u592a\u591a\u7684\u7814\u8ba8\u4f1a, \u7ed3\u679c\u5c31\u662f\u4eba\u4eec\u8fde\u4e00\u4e2a\u4e5f\u6ca1\u53c2\u52a0\u3002\u5047\u8bbe\u53ea\u6709\u4e24\u4e2a\u7814\u8ba8\u4f1a, \u90a3\u4e48\u6bcf\u4e2a\u4eba\u4f1a\u89c9\u5f97\u4ed6\u5fc5\u987b\u53bb; \u4f46\u5982\u679c\u592a\u591a\u7684\u8bdd, \u4f60\u5219\u4f1a\u5f00\u59cb\u8ba4\u4e3a\u6ca1\u6709\u65f6\u95f4\u53bb\u53c2\u52a0\u5168\u90e8\u7684\u7814\u8ba8\u4f1a, \u800c\u51b3\u5b9a\u4e0d\u53bb\u4efb\u4f55\u4e00\u4e2a\u3002\u4f46\u5728\u53e6\u4e00\u65b9\u9762\u8fd9\u6837\u5bf9\u5b66\u751f\u662f\u6709\u597d\u5904\u7684, \u56e0\u4e3a\u4ed6\u4eec\u80fd\u5b66\u4e60\u8bb8\u591a\u4e0d\u540c\u7684\u9886\u57df\u548c\u89c2\u70b9\u3002
\n\u5218<\/strong>: \u5f88\u591a\u5e74\u524d, \u6211\u8bfb\u5230\u4e00\u7bc7S. Hilderbrant \u5199\u7684\u6587\u7ae0, \u63cf\u8ff0\u5728\u5fb7\u56fdOberwolfach \u7684\u4e00\u4e9b\u6d3b\u52a8\u3002\u4f60\u80fd\u8c08\u8c08\u8fd9\u4e2a\u5417?
\nG<\/strong>: \u4ece70\u5e74\u4ee3\u4e2d\u671f\u523090\u5e74\u4ee3\u4e2d\u671f, \u6bcf2\u5e74\u6211\u90fd\u53c2\u52a0\u5728Oberwolfach \u6240\u4e3e\u884c\u7684\u53d8\u5206\u5b66(Calculusof Variations) \u4f1a\u8bae\u3002\u73b0\u5728\u7684Oberwolfach \u751a\u81f3\u662f\u6bd4\u4ece\u524d\u66f4\u4e3a\u6d3b\u8dc3, \u4e14\u5173\u4e8e\u53d8\u5206\u5b66\u7684\u4f1a\u8bae\u4e5f\u8fd8\u6301\u7eed\u5728\u8fdb\u884c\u4e2d\u3002\u5728\u4ece\u524d\u521a\u5f00\u59cb\u65f6, \u4e0e\u4f1a\u8005\u4e0d\u591a, \u5927\u90e8\u5206\u662f\u4ece\u4e8b\u76f8\u540c\u9886\u57df\u7684\u7814\u7a76\u3002\u65e9\u4e0a\u901a\u5e38\u6709\u4e00\u4e9b\u6f14\u8bb2, \u800c\u4e0b\u5348\u5219\u53ea\u662f\u76f8\u4e92\u4ea4\u8c08, \u6216\u662f\u8ba8\u8bba\u95ee\u9898, \u6216\u662f\u804a\u5929, \u6709\u8bb8\u591a\u81ea\u7531\u7684\u65f6\u95f4\u3002\u90a3\u662f\u975e\u5e38\u5730\u6709\u542f\u53d1\u6027\u3002\u8fd1\u6765, \u505a\u53d8\u5206\u5b66\u7684\u4eba\u6108\u6765\u6108\u591a\u3002\u572870\u5e74\u4ee3\u65f6, Oberwolfach \u7684\u4e00\u573a\u4f1a\u8bae\u5927\u7ea6\u4f1a\u670925\u81f330\u4e2a\u4e0e\u4f1a\u8005, \u4f46\u73b0\u4eca\u5219\u53ef\u591a\u8fbe70\u4eba\u3002\u7ed3\u679c\u5c31\u662f\u5728\u65e9\u4e0a\u548c\u4e0b\u5348\u90fd\u6709\u5f88\u591a\u7684\u6f14\u8bb2\u3002\u4e0d\u8fc7\u5f53\u7136, \u4e00\u4e2a\u5927\u578b\u7684\u4f1a\u8bae\u603b\u6709\u5176\u4f18\u70b9\u548c\u7f3a\u70b9\u3002\u8fd8\u6709\u6211\u8ba4\u4e3a\u4ece70\u81f380\u5e74\u4ee3\u7684\u751f\u6d3b\u662f\u7a0d\u4e3a\u95f2\u9038\u7684, \u4f8b\u5982\u5728\u90a3\u6bb5\u671f\u95f4\u6211\u4ece\u6765\u6ca1\u6709\u4efb\u4f55\u53d1\u8868\u8bba\u6587\u7684\u538b\u529b\u3002\u90a3\u65f6\u867d\u7136\u6ca1\u6709\u592a\u591a\u7684\u6559\u804c\u4e0d\u8fc7\u5374\u591f\u591a, \u6240\u4ee5\u4eba\u4eec\u6709\u673a\u4f1a\u53bb\u5f97\u5230\u4e00\u4e2a\u5de5\u4f5c\u800c\u540e\u518d\u53bb\u8c0b\u5f97\u66f4\u597d\u7684\u804c\u4f4d\u3002\u540e\u6765\u751a\u81f3\u53d8\u5f97\u4e0d\u592a\u56f0\u96be\u53bb\u5f97\u5230\u4e00\u4e2a\u6559\u804c\u3002\u73b0\u5728\u5462, \u6709\u80a1\u5f88\u5f3a\u7684\u538b\u529b\u8feb\u4f7f\u5e74\u8f7b\u4eba\u8981\u53d1\u8868\u6587\u7ae0, \u6211\u60f3\u8fd9\u662f\u4e0d\u597d\u7684\u3002\u6211\u66fe\u8dfb\u8eab\u67d0\u4e9b\u6559\u5e08\u9074\u9009\u59d4\u5458\u4f1a, \u770b\u5230\u6709\u5e74\u8f7b\u4eba\u53d1\u8868\u56db\u3001 \u4e94\u5341\u7bc7\u8bba\u6587\u3002\u5f53\u7136\u603b\u662f\u4f1a\u6709\u4e9b\u4f8b\u5916\u7684\u4eba, \u4f46\u662f\u6709\u4e9b\u65f6\u5019, \u51fa\u7248\u7684\u6587\u7ae0\u770b\u8d77\u6765\u53ea\u50cf\u662f\u4e2a\u7cbe\u7ec3\u7684\u4e60\u9898\u6216\u8005\u662f\u4e9b\u53ea\u4f1a\u8ba9\u5c11\u6570\u4eba\u4ea7\u751f\u5174\u8da3\u7684\u7e41\u7410\u7ec6\u8282\u3002\u6211\u4e0d\u8ba4\u4e3a\u8fd9\u5bf9\u6570\u5b66\u800c\u8a00\u662f\u6b63\u9762\u7684, \u56e0\u4e3a\u901a\u5e38\u592a\u591a\u7684\u7ec6\u8282\u65e0\u52a9\u4e8e\u5bf9\u95ee\u9898\u7684\u4e86\u89e3\u3002\u4e00\u4e2a\u540e\u679c\u5c31\u662f\u4eba\u4eec\u8f83\u5c11\u6709\u65f6\u95f4\u53bb\u5bf9\u8bdd, \u6bcf\u4e2a\u4eba\u53ea\u4e13\u6ce8\u4e8e\u4ed6\u81ea\u5df1\u7684\u95ee\u9898\u3002\u6216\u8bb8\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u6211\u4eec\u4f1a\u6709\u5982\u6b64\u591a\u7684\u671f\u520a\u548c\u6570\u4ee5\u5343\u8ba1\u7684\u8bba\u6587\u3002\u8c01\u4f1a\u53bb\u8bfb\u8fd9\u4e48\u591a\u5462? \u542c\u8d77\u6765\u7b80\u76f4\u662f\u4e0d\u53ef\u80fd\u3002\u5f53\u6211\u5f00\u59cb\u6211\u7684\u5b66\u672f\u751f\u6daf\u65f6, \u90a3\u65f6\u53ea\u6709\u5c11\u6570\u91cd\u8981\u7684\u671f\u520a\u3002\u4eba\u4eec\u7684\u4e60\u60ef\u5927\u6982\u662f\u4e00\u5e74\u53d1\u8868\u4e00\u7bc7\u8bba\u6587, \u6bcf\u4e24\u5e74\u53c2\u52a0\u4e00\u6b21\u5b66\u672f\u4f1a\u8bae\u3002\u73b0\u5728\u5219\u6709\u597d\u591a\u5b66\u672f\u4f1a\u8bae, \u800c\u6f14\u8bb2\u8005\u5c31\u88ab\u8feb\u91cd\u8986\u76f8\u540c\u7684\u8bb2\u9898\u6216\u7a0d\u505a\u53d8\u5316\u3002\u53e6\u4e00\u65b9\u9762, \u6211\u4e86\u89e3\u5e74\u8f7b\u4eba\u627f\u53d7\u5230\u538b\u529b, \u800c\u53c2\u52a0\u4f1a\u8bae\u5bf9\u4ed6\u4eec\u800c\u8a00\u662f\u4e2a\u673a\u4f1a\u3002\u5bf9\u4e8e\u8fd9,\u6211\u770b\u4e0d\u5230\u597d\u7684\u89e3\u51b3\u65b9\u6cd5\u3002\u6216\u8bb8\u6211\u4eec\u6570\u5b66\u5bb6\u662f\u592a\u591a\u4e86, \u6211\u4e0d\u6653\u5f97\u3002\u6211\u771f\u7684\u4e0d\u662f\u5b8c\u5168\u4e86\u89e3\u8fd9\u6837\u7684\u673a\u5236, \u4f46\u786e\u5b9a\u7684\u662f\u5bf9\u5e74\u8f7b\u7684\u6570\u5b66\u5bb6\u800c\u8a00\u8fd9\u662f\u56f0\u96be\u7684\u3002\u8fd9\u4e5f\u5f15\u8d77\u4e86\u4e9b\u95ee\u9898, \u4f8b\u5982\u4e0e\u5176\u5b83\u9886\u57df\u7684\u8054\u7cfb\u53d8\u5f97\u5c11\u4e86\u3002\u6570\u5b66\u5bb6\u66fe\u4e60\u4e8e\u548c\u7269\u7406\u5b66\u5bb6\u3001 \u81ea\u7136\u79d1\u5b66\u5bb6\u3001 \u751f\u7406\u5b66\u5bb6\u7b49\u5171\u4e8b, \u73b0\u5728\u6211\u4eec(\u6570\u5b66\u5bb6) \u6216\u8bb8\u4ecd\u4e0e\u4ed6\u4eec\u4ea4\u8c08, \u4f46\u4e0d\u7531\u5730\u6211\u4eec\u4f1a\u7acb\u523b\u8fdc\u79bb\u4ed6\u4eec\u7684\u95ee\u9898, \u8fd8\u662f\u5f52\u7ed3\u5230\u6211\u4eec\u81ea\u5df1\u7684\u65b9\u5f0f\u3002\u8fd9\u662f\u6211\u7684\u611f\u89c9, \u4e0d\u8fc7\u6216\u8bb8\u5b8c\u5168\u662f\u9519\u8bef\u7684\u3002
\n\u5218<\/strong>: \u662f\u554a! \u6211\u4e5f\u4e0e\u4f60\u6709\u76f8\u540c\u7684\u611f\u89c9\u3002
\nG<\/strong>: \u5bf9\u6211\u800c\u8a00, \u8fd9\u4e9b\u4e8b\u770b\u8d77\u6765\u5bf9\u6570\u5b66\u800c\u8a00\u4e0d\u662f\u6b63\u9762\u7684\u3002
\n\u5218<\/strong>: \u4f60\u77e5\u9053\u53f0\u6e7e\u5e74\u8f7b\u4eba\u901a\u5e38\u662f\u5f88\u96be\u548c\u8d44\u6df1\u7684\u957f\u8f88\u8bf4\u8bdd\u7684\u5417?
\nG<\/strong>: \u54e6, \u5728\u6bd4\u8428\u4e0d\u662f\u90a3\u4e48\u96be\u7684\u3002\u56e0\u4e3a\u6bd4\u8428\u662f\u4e00\u4e2a\u5f88\u5c0f\u7684\u57ce\u9547, \u5927\u7ea6\u670910\u4e07\u5c45\u6c11\u4e14\u5927\u591a\u6570\u4e0d\u662f\u4f4f\u5728\u5e02\u4e2d\u5fc3, \u56e0\u6b64\u5728\u5e02\u4e2d\u5fc3\u5f88\u591a\u65f6\u5019\u4f60\u4f1a\u9047\u5230\u7684\u662f\u5b66\u751f\u548c\u6559\u5e08\u3002\u4ed6\u4eec\u5c31\u5728\u90a3\u513f\u3002\u8b6c\u5982\u8bf4\u6211, \u73b0\u5728\u6211\u4f4f\u5728\u4f5b\u7f57\u4f26\u65af, \u6bcf\u661f\u671f\u901a\u8f66\u5230\u6bd4\u8428, \u5728\u90a3\u513f\u5f85\u4e09\u3001 \u56db\u5929\u3002\u5f53\u6211\u5728\u90a3\u513f\u65f6, \u4ece\u65e9\u4e0a\u516b\u70b9\u5230\u665a\u4e0a\u5341\u3001 \u5341\u4e00\u70b9\u6211\u6216\u662f\u5728\u6211\u529e\u516c\u5ba4\u3001 \u6216\u548c\u67d0\u4eba\u4e00\u8d77\u5de5\u4f5c\u3001 \u6216\u662f\u78b0\u89c1\u67d0\u4eba\u4e00\u8d77\u53bb\u665a\u9910\u3002\u5927\u591a\u65f6\u5019,\u8fd9\u4e2a\u4eba\u662f\u540c\u4e8b\u6216\u5b66\u751f\u3002\u4e0d\u5355\u662f\u535a\u58eb\u73ed\u5b66\u751f, \u5927\u5b66\u90e8\u5b66\u751f\u548c\u6559\u6388\u4eec\u4ea4\u8c08\u4e5f\u4e0d\u56f0\u96be\u3002\u6211\u5fc5\u987b\u8bf4\u7684\u662f\u6216\u8bb8\u5728\u6570\u5b66\u65b9\u9762\u6bd4\u8428\u662f\u610f\u5927\u5229\u7684\u4e00\u4e2a\u7279\u6b8a\u7684\u5730\u65b9\u3002\u8fd9\u6709\u7740\u4e24\u4e16\u7eaa\u7684\u4f20\u7edf, \u800c\u5176\u4e2d\u7684\u4e00\u4e2a\u7f18\u6545\u6216\u8bb8\u662f\u56e0\u4e3a\u9ad8\u7b49\u5e08\u8303\u5b66\u6821\u3002\u8fd9\u95f4\u5b66\u6821\u7f51\u7f57\u4e86\u2014\u6211\u4eec\u4e0d\u80fd\u8bf4\u6700\u597d, \u4f46\u80af\u5b9a\u662f\u5728\u610f\u5927\u5229\u7684\u4e00\u4e9b\u6700\u597d\u7684\u5b66\u751f\u3002\u4e8b\u5b9e\u4e0a,\u8fd9\u662f\u552f\u4e00\u4e00\u4e2a\u5b66\u751f\u4eec\u987b\u901a\u8fc7\u975e\u5e38\u4e25\u5cfb\u7684\u7ade\u4e89\u5e76\u53ef\u5f97\u5230\u5b66\u8d39\u548c\u751f\u6d3b\u8d39\u7684\u8865\u52a9\u540c\u65f6\u8fd8\u6709\u96f6\u7528\u94b1\u7684\u5730\u65b9, \u5f53\u7136\u66f4\u4e0d\u7528\u8bf4\u6709\u989d\u5916\u7684\u8bfe\u7a0b, \u8fd8\u53ef\u4ee5\u76f4\u63a5\u548c\u6559\u6388\u63a5\u89e6\u3002\u6240\u4ee5\u7279\u522b\u5438\u5f15\u597d\u7684\u5b66\u751f, \u5c24\u5176\u662f\u597d\u7684\u6570\u5b66\u5b66\u751f\u3002\u4e5f\u56e0\u6b64, \u5927\u591a\u6570\u7684\u597d\u5b66\u751f\u90fd\u4f1a\u53c2\u52a0\u7ade\u8bd5\u4ee5\u6c42\u8fdb\u5165\u672c\u6821\u3002\u4e0d\u8fc7, \u73b0\u4eca\u5b66\u751f\u5927\u6982\u89c9\u5f97\u5927\u57ce\u5e02\u66f4\u5177\u6709\u5438\u5f15\u529b\u3002\u8fd8\u6709\u6211\u4e0d\u592a\u786e\u5b9a\u662f\u5426\u6240\u6709\u60f3\u5ff5\u6570\u5b66\u7684\u597d\u5b66\u751f\u771f\u7684\u6765\u5ff5\u6570\u5b66\u4e86\u3002\u5e38\u5e38, \u4ed6\u4eec\u9009\u62e9\u5176\u5b83\u4e0d\u540c\u7684\u79d1\u76ee\u3002\u5728\u6211\u5ff5\u5927\u5b66\u7684\u65f6\u5019, \u5c31\u85aa\u8d44\u800c\u8a00, \u6210\u4e3a\u4e00\u4e2a\u6570\u5b66\u5bb6\u6216\u5de5\u7a0b\u5e08\u5e76\u65e0\u5982\u6b64\u5927\u7684\u5dee\u5f02, \u4f46\u662f\u4f60\u4ee5\u540e\u83b7\u5f97\u7684\u81ea\u7531\u548c\u4f60\u80fd\u591f\u4ece\u4e8b\u4f60\u771f\u6b63\u559c\u6b22\u505a\u7684\u4e8b\u5f25\u8865\u4e86\u8fd9\u79cd\u5dee\u5f02\u3002\u73b0\u5728, \u4e0d\u518d\u662f\u8fd9\u6837\u4e86, \u5728\u610f\u5927\u5229\u5927\u5b66\u7684\u85aa\u6c34\u6bd4\u8d77\u4f8b\u5982\u79c1\u4eba\u4f01\u4e1a\u6765\u4e0d\u662f\u90a3\u4e48\u9ad8\u3002\u800c\u6211\u76f8\u4fe1\u5982\u679c\u4f60\u6570\u5b66\u5f88\u597d, \u4f60\u6216\u8bb8\u53ef\u4ee5\u5728\u5de5\u7a0b\u65b9\u9762\u4e00\u6837\u5730\u597d, \u4e3a\u4f55\u4e0d\u53ef? \u6ca1\u6709\u4ec0\u4e48\u7406\u7531\u8bf4\u4e00\u4e2a\u4eba\u53ea\u80fd\u5728\u4e00\u4ef6\u4e8b\u4e0a\u5f88\u597d\u3002\u4e8b\u5b9e\u4e0a, \u8fd9\u5c31\u662f\u6211\u603b\u662f\u544a\u8bc9\u5b66\u751f\u7684, \u8981\u4ed6\u4eec\u4e0d\u5e94\u628a\u5174\u8da3\u53ea\u5c40\u9650\u5728\u6570\u5b66\u4e0a, \u4ed6\u4eec\u5e94\u8bd5\u7740\u62d3\u5c55\u5230\u66f4\u5e7f\u7684\u5c42\u9762\u3002\u6211\u7684\u770b\u6cd5\u662f, \u5982\u679c\u4f60\u53d7\u5230\u975e\u5e38\u597d\u7684\u6570\u5b66\u8bad\u7ec3, \u4f60\u4e00\u5b9a\u80fd\u591f\u6210\u4e3a\u4e00\u4e2a\u597d\u7684, \u6bd4\u5982\u8bf4, \u7ba1\u7406\u4eba\u624d\u3002
\n\u5218<\/strong>: \u521a\u521a\u6211\u63d0\u5230\u5e74\u8f7b\u4eba\u4e0e\u6559\u6388\u4ea4\u8c08\u6709\u56f0\u96be, \u6211\u5e76\u4e0d\u662f\u6307\u4ed6\u4eec\u6ca1\u6709\u673a\u4f1a\u53bb\u8c08\u3002\u4ed6\u4eec\u6709\u673a\u4f1a, \u5f88\u591a\u673a\u4f1a\u3002\u901a\u5e38, \u8fd9\u79cd\u96be\u5904\u6765\u81ea\u4ed6\u4eec\u81ea\u5df1, \u4ed6\u4eec\u5bb3\u6015\u53bb\u8bf4\u3002
\nG<\/strong>: \u54e6, \u8fd9\u5728\u610f\u5927\u5229\u4e5f\u662f\u4e00\u6837, \u5b66\u751f\u4eec\u5bb3\u6015\u8bf4\u8bdd\u3002\u4ed6\u4eec\u6709\u673a\u4f1a, \u4f46\u662f\u5bb3\u6015\u3002
\n\u9648<\/strong>: \u4ed6\u4eec\u5bb3\u6015\u8bf4\u8bdd\u53ea\u662f\u5728\u8c08\u8bba\u6570\u5b66\u65f6\u6216\u8005\u662f\u5728\u6240\u6709\u7684\u60c5\u51b5\u4e0b\u90fd\u5982\u6b64?
\nG<\/strong>: \u6211\u60f3\u662f\u5728\u6240\u6709\u7684\u60c5\u51b5\u4e0b! \u4e00\u4e2a\u7406\u7531\u6216\u8bb8\u662f\u5e74\u9f84\u53ca\u804c\u4f4d\u7684\u5dee\u522b\u3002\u5b66\u751f\u901a\u5e38\u8f83\u559c\u597d\u548c\u52a9\u7406\u800c\u975e\u548c\u6559\u6388\u4eec\u4ea4\u8c08, \u56e0\u4e3a\u4ed6\u4eec\u591a\u5c11\u5e74\u7eaa\u76f8\u4eff\u3002\u6211\u8ba4\u4e3a\u53e6\u4e00\u4e2a\u7406\u7531\u662f\u56e0\u4e3a\u8003\u8bd5\u8fd9\u4e2a\u7cfb\u7edf\u3002\u4ed6\u4eec\u6653\u5f97\u4ed6\u4eec\u5fc5\u987b\u901a\u8fc7\u8003\u8bd5, \u6240\u4ee5\u4e0d\u613f\u5c55\u793a\u81ea\u6211\u3002\u4ed6\u4eec\u603b\u5bb3\u6015\u4f60\u4f1a\u7531\u6b64\u53bb\u8861\u91cf\u4ed6\u4eec, \u800c\u6211\u8ba4\u4e3a\u8fd9\u6709\u65f6\u5019\u751a\u81f3\u4e5f\u771f\u662f\u5982\u6b64\u3002
\n\u9648<\/strong>: \u6bcf\u6b21\u6211\u53bb\u89c1\u6211\u6307\u5bfc\u8001\u5e08\u7684\u65f6\u5019, \u603b\u5e0c\u671b\u81ea\u5df1\u51c6\u5907\u5f97\u5f88\u597d\u3002 (\u4f17\u7b11!)
\nG<\/strong>: \u4e0d\u8fc7, \u8eab\u4e3a\u5b66\u751f, \u4f60\u662f\u4f1a\u5bb3\u6015\u7684\u3002\u6211\u4e0d\u80fd\u8bf4\u6211\u603b\u662f\u6709\u51c6\u5907\u7684\u3002\u6211\u559c\u6b22\u4e0e\u4eba\u5408\u4f5c, \u4e0d\u559c\u6b22\u5355\u6253\u72ec\u6597, \u56e0\u4e3a\u90a3\u6bd4\u8f83\u6709\u8da3\u3002\u4e0d\u8fc7\u6211\u65f6\u5e38\u6709\u4e9b\u611a\u8822\u7684\u6570\u5b66\u9648\u8ff0\u6216\u662f\u4e9b\u4e0d\u6b63\u786e\u7684\u8bc1\u660e\u3002\u8fd9\u6216\u8bb8\u4ece\u4e0d\u4f1a\u53d1\u751f\u5728\u597d\u7684\u6570\u5b66\u5bb6\u8eab\u4e0a, \u4f46\u5374\u7ecf\u5e38\u53d1\u751f\u5728\u6211\u8eab\u4e0a\u3002
\n\u9648<\/strong>: \u4f60\u80fd\u591f\u63d0\u4e00\u4e9b\u5728\u53d8\u5206\u5b66\u4e0a\u672a\u89e3\u51b3\u7684\u95ee\u9898\u6216\u65b0\u7684\u7814\u7a76\u65b9\u5411\u5417?
\nG<\/strong>: \u55ef, \u53d8\u5206\u5b66\u53ef\u8bf4\u662f\u67d0\u4e9b\u95ee\u9898\u548c\u65b9\u6cd5\u7684\u96c6\u5408, \u5f88\u96be\u6307\u51fa\u597d\u7684\u5f85\u89e3\u7684(good open) \u65b9\u5411\u3002\u4f46\u6211\u60f3\u4e00\u4e2a\u4e3b\u8981\u7684\u65b9\u5411\u662f\u53bb\u4e86\u89e3\u7275\u6d89\u5230\u975e\u7eaf\u91cf\u51fd\u6570(non-scalar functions) \u7684\u53d8\u5206\u95ee\u9898, \u597d\u6bd4\u8bf4\u50cf\u8c03\u548c\u6620\u5c04(harmonic mappings), \u6768\u2013\u7c73\u5c14\u65af\u6cdb\u51fd(Yang-Mill\u2019s functional) \u53ca\u4e00\u4e9b\u63cf\u8ff0\u7ec6\u5fae\u7ed3\u6784\u7684\u7269\u7406\u6a21\u578b\u7b49\u7b49\u7684\u51e0\u4f55\u53d8\u5206(geometric variational) \u95ee\u9898\u3002\u8fd9\u4e9b\u95ee\u9898\u7684\u5171\u901a\u5904\u662f\u4f1a\u6709\u5947\u5f02\u70b9(singularities) \u4ea7\u751f\u3002\u8fd9\u4e9b\u5947\u5f02\u6027\u662f\u91cd\u8981\u7684, \u6709\u65f6\u5019\u5947\u5f02\u89e3(singularsolutions) \u751a\u81f3\u6bd4\u5e73\u6ed1\u89e3(smooth solutions) \u66f4\u4e3a\u91cd\u8981\u3002\u660e\u4e86\u8fd9\u79cd\u5947\u5f02\u70b9, \u5b83\u4eec\u5982\u4f55\u4ea7\u751f,\u7ed3\u6784\u5982\u4f55, \u662f\u975e\u5e38\u91cd\u8981\u7684\u8bfe\u9898\u3002
\n\u9648<\/strong>: \u81f3\u4e8e\u6709\u4e9b\u8001\u7684\u4f46\u4ecd\u65e7\u91cd\u8981\u7684\u95ee\u9898\u5462?
\nG<\/strong>: \u6709\u5f88\u591a\u60ac\u800c\u672a\u51b3\u7684\u8001\u95ee\u9898, \u4f8b\u5982\u5bf9\u6781\u5c0f\u66f2\u9762\u7684\u5b64\u7acb(isolated) \u5947\u5f02\u70b9\u505a\u5206\u7c7b, \u6216\u662f\u7814\u7a76\u8f83\u9ad8\u4f59\u7ef4(co-dimensional) \u7684\u6781\u5c0f\u66f2\u9762\u6216\u56fe\u5f62(graph)\u3002
\n\u9648<\/strong>: \u4f60\u63d0\u5230\u4e86\u6781\u5c0f\u7ec4\u6001(minimal configuration)\u3002\u4e3a\u4f55\u6211\u4eec\u603b\u8bd5\u7740\u8981\u627e\u5230\u6781\u5c0f\u7ec4\u6001\u800c\u975e\u5b9a\u6001(stationary configuration) \u5462?
\nG<\/strong>: \u6216\u8bb8\u662f\u56e0\u4e3a\u5b83\u6bd4\u8f83\u7b80\u5355\u5427\u3002\u53e6\u5916, \u6781\u5c0f\u89e3(minimizer) \u6709\u8f83\u5f3a\u7684\u6027\u8d28\u3002\u4f8b\u5982\u6709\u4e0e\u7269\u7406\u76f8\u5173\u7684\u80fd\u91cf\u6cdb\u51fd, \u5176\u4e34\u754c\u70b9(critical points) \u5728\u6240\u6709\u7684\u5730\u65b9\u90fd\u662f\u5947\u5f02\u7684, \u7136\u800c\u6781\u5c0f\u89e3\u53ea\u5728\u4e9b\u8f83\u4f4e\u7ef4\u5ea6\u7684\u96c6\u5408\u624d\u662f\u5947\u5f02\u7684\u3002\u6709\u4e9b\u65f6\u5019, \u6781\u5c0f\u6027(minimality) \u53ef\u7528\u4e00\u4e9b\u7a33\u5b9a\u6027(stability) \u6765\u53d6\u4ee3\u3002
\n\u9648<\/strong>: \u6216\u8bb8\u4f60\u80fd\u591f\u89e3\u7b54\u6211\u5fc3\u4e2d\u7684\u4e00\u4e2a\u95ee\u9898, \u4e3a\u4ec0\u4e48\u5728\u7269\u7406\u7684\u4e16\u754c\u4e2d\u5e38\u5b58\u5728\u53d8\u5206\u539f\u7406(variational principle)? \u4f60\u7684\u89c2\u70b9\u662f\u5982\u4f55\u5462?
\nG<\/strong>: \u6211\u60f3\u4f60\u7684\u95ee\u9898\u53ef\u4ee5\u5f88\u591a\u65b9\u6cd5\u6765\u56de\u7b54\u3002\u6211\u4eec\u53ef\u4ee5\u50cf\u4ece\u524d\u4e00\u6837\u8bf4\u4e0a\u5e1d\u4ee5\u53ef\u80fd\u7684\u6700\u4f73\u7684\u65b9\u6cd5\u53bb\u521b\u9020\u5b87\u5b99\u4e2d\u7684\u6bcf\u4e2a\u4e8b\u7269; \u6216\u8005\u6211\u4eec\u53ef\u4ee5\u8bf4\u6570\u5b66\u5c31\u662f\u5982\u6b64\u5730\u8fd0\u4f5c; \u6216\u8005\u6211\u4eec\u53ef\u4ee5\u8bf4\u5f53\u6211\u4eec\u5c1d\u8bd5\u53bb\u89e3\u91ca\u81ea\u7136\u73b0\u8c61\u65f6, \u6211\u4eec\u5bfb\u6c42\u7684\u662f\u4e9b\u7b80\u5355\u7684\u539f\u7406, \u800c\u6781\u5c0f\u539f\u7406(minimum principle) \u662f\u4e2a\u975e\u5e38\u7b80\u5355\u7684\u539f\u7406\u3002
\n\u9648<\/strong>: \u8fd9\u76f8\u5f53\u50cf\u8bb8\u591a\u6570\u5b66\u6216\u7269\u7406\u5b66\u5bb6\u6240\u559c\u7231\u7684\u6240\u8c13\u7b80\u7ea6\u6027(simplicity)\u2026
\nG<\/strong>: \u662f\u7684! \u53ef\u80fd\u662f\u76f8\u540c\u7684\u6cd5\u5219\u3002\u5047\u4f7f\u6211\u4eec\u4ee5\u4e00\u4e2a\u7e41\u590d\u7684\u539f\u7406\u4e3a\u57fa\u7840\u6765\u89e3\u91ca\u67d0\u4e9b\u4e8b\u60c5, \u6211\u4eec\u5e76\u6ca1\u6709\u89e3\u91ca\u5f97\u5f88\u591a, \u56e0\u4e3a\u6211\u4eec\u4e8b\u5b9e\u4e0a\u6216\u8bb8\u662f\u5728\u7528\u6bd4\u8981\u89e3\u91ca\u7684\u4e8b\u60c5\u66f4\u4e3a\u590d\u6742\u7684\u4e8b\u7269\u53bb\u89e3\u91ca\u8be5\u4e8b\u7269\u3002(\u4f17\u7b11!)\u56de\u5230\u4f60\u7684\u95ee\u9898, \u6211\u60f3\u6709\u5f88\u591a\u3001 \u5f88\u591a\u7684\u7b54\u6848, \u800c\u771f\u6b63\u7684\u7b54\u6848\u53ef\u80fd\u5c31\u5728\u5386\u53f2\u4e2d: \u53d8\u5206\u539f\u7406\u5df2\u7ecf\u8fd0\u4f5c\u4e86\u51e0\u4e2a\u51e0\u4e16\u7eaa\u4e86\u3002\u6211\u60f3\u79d1\u5b66\u53f2\u5c31\u7ed9\u4e86\u7b54\u6848\u4e86, \u4e0d\u53ea\u5728\u6570\u5b66\u91cc, \u4e8b\u5b9e\u4e0a\u4f60\u770b\u5230\u66f4\u591a\u6781\u5c0f\u539f\u7406\u5728\u7269\u7406\u53f2\u4e0a\u3002\u8bf4\u5230\u8fd9\u91cc, \u4f60\u521a\u521a\u95ee\u6211\u5173\u4e8e\u53d8\u5206\u5b66\u53ef\u80fd\u7684\u53d1\u5c55\u65b9\u5411, \u60f3\u60f3\u770b\u62c9\u683c\u6717\u65e5(La-grangian) \u548c\u54c8\u5bc6\u5c14\u987f(Hamiltonian) \u7406\u8bba, \u5728\u9002\u5f53\u7684\u6761\u4ef6\u4e0b, \u4e24\u8005\u662f\u7b49\u4ef7\u7684\u3002\u6ca1\u6709\u4e86\u8fd9\u4e9b\u6761\u4ef6, \u6211\u4eec\u662f\u5426\u53ef\u7528\u5f31\u4e00\u70b9\u7684\u65b9\u5f0f\u53bb\u5173\u8fde\u4ed6\u4eec?
\n\u5218<\/strong>: \u5728\u610f\u5927\u5229, \u662f\u4ece\u516d\u5c81\u5f00\u59cb\u4e0a\u5c0f\u5b66\u5417?
\nG<\/strong>: \u662f\u7684, \u516d\u5c81\u3002\u4f46\u662f\u6709\u5021\u8bae\u6539\u6210\u5141\u8bb8\u4e94\u5c81\u5165\u5c0f\u5b66\u7684\u63d0\u6848\u3002\u76ee\u524d\u5b69\u7ae5\u516d\u5c81\u5165\u5b66, \u8bfb\u4e86\u4e94\u5e74\u5c0f\u5b66\u540e,\u63a5\u7740\u662f\u4e09\u5e74\u7684\u521d\u4e2d\u548c\u4e94\u5e74\u7684\u9ad8\u4e2d\u3002\u4eca\u5e74\u5f00\u59cb, \u5728\u5927\u5b66\u65bd\u884c\u65b0\u7684\u5236\u5ea6: \u4fee\u4e1a\u4e09\u5e74\u5f97\u7b2c\u4e00\u4e2a\u5b66\u4f4d,\u518d\u4e8c\u5e74\u5f97\u7b2c\u4e8c\u4e2a\u5b66\u4f4d, \u7136\u540e\u518d\u7ecf\u4e09\u5e74\u5f97\u5230\u535a\u58eb\u5b66\u4f4d\u3002
\n\u5218<\/strong>: \u5b66\u751f\u5728\u5c0f\u5b66\u65f6\u53ea\u5b66\u610f\u5927\u5229\u6587, \u6216\u8005\u8fd8\u5b66\u5176\u5b83\u8bed\u6587?
\nG<\/strong>: \u9664\u610f\u5927\u5229\u6587\u5916, \u73b0\u5728\u4ece\u4e09\u5e74\u7ea7\u8d77, \u4ed6\u4eec\u5f00\u59cb\u975e\u6b63\u5f0f\u5730\u5b66\u4e00\u79cd\u5916\u56fd\u8bed\u6587, \u6211\u60f3\u6b63\u5f0f\u5f00\u59cb\u5b66\u662f\u5728\u521d\u4e2d\u65f6\u3002\u6709\u4e9b\u5b66\u6821\u53ef\u5141\u8bb8\u5b66\u751f\u9009\u62e9\u4e24\u79cd\u5916\u8bed\u3002\u8bfe\u7a0b\u89c4\u5b9a\u5728\u610f\u5927\u5229\u7684\u5b66\u6821\u662f\u975e\u5e38\u4e25\u7684, \u4e2d\u5b66\u91cc\u5b66\u751f\u6ca1\u6709\u9009\u62e9\u79d1\u76ee\u7684\u6743\u5229, \u6240\u6709\u7684\u8bfe\u7a0b\u90fd\u662f\u56fa\u5b9a\u7684\u3002\u5982\u679c\u6709\u6559\u7b2c\u4e8c\u5916\u8bed\u7684\u8bdd, \u901a\u5e38\u662f\u5728\u6b63\u89c4\u7684\u8bfe\u7a0b\u5916, \u5728\u4e0b\u5348\u52a0\u51e0\u4e2a\u5c0f\u65f6\u7684\u8bfe\u3002\u8fc7\u53bb, \u5b66\u751f\u901a\u5e38\u662f\u5b66\u6cd5\u6587, \u4f46\u73b0\u5728\u591a\u534a\u8981\u6c42\u5b66\u82f1\u6587\u3002\u4f46\u5b66\u6821\u91cc\u6709\u4e9b\u6559\u6cd5\u6587\u4f46\u53c8\u4e0d\u80fd\u591f\u88ab\u88c1\u6389\u7684\u8001\u5e08, \u6240\u4ee5\u6709\u4e9b\u5b66\u751f\u5fc5\u987b\u5b66\u6cd5\u6587! (\u4f17\u7b11!) \u4f46\u662f\u901a\u5e38\u5b66\u6cd5\u6587\u7684\u5b66\u751f\u4e5f\u5b66\u82f1\u6587\u7684\u3002\u7ed3\u679c\u4ed6\u4eec\u5b66\u4e24\u79cd\u5916\u56fd\u8bed\u6587, \u8fd9\u662f\u597d\u4e8b\u3002
\n\u5218<\/strong>: \u53f0\u6e7e\u5b66\u751f\u5728\u521d\u4e2d\u65f6\u5f00\u59cb\u5b66\u82f1\u6587, \u73b0\u5728\u4e5f\u8bd5\u7740\u5728\u5c0f\u5b66\u91cc\u529e\u3002\u5bf9\u4e8e\u8fd9, \u4f60\u7684\u770b\u6cd5\u5982\u4f55?
\nG<\/strong>: \u6211\u8ba4\u4e3a\u5f88\u597d\u7684\u3002\u4f8b\u5982\u8bf4\u5728\u6211\u5ff5\u4e66\u65f6\u4e5f\u6709\u5916\u8bed, \u4f46\u4e3b\u8981\u662f\u5b66\u5386\u53f2\u548c\u6587\u5b66\u800c\u4e14\u5f88\u5c11\u8bb2\u3002\u5b66\u751f\u88ab\u8981\u6c42\u5b66\u4e60\u6240\u6709\u7684\u89c4\u5219\u548c\u6240\u6709\u7684\u4f8b\u5916\u7b49\u7b49\u3002\u4f46\u73b0\u5728\u60c5\u51b5\u662f\u6709\u6539\u53d8\u4e86\u3002\u6211\u4ecd\u65e7\u8bb0\u5f97\u5728\u6cd5\u6587\u91cc\u5934\u7684\u4e0d\u540c\u7684\u89c4\u5219\u548c\u4f8b\u5916, \u4f46\u662f\u6211\u5b66\u5230\u7684\u5355\u5b57\u4e0d\u591a\u3002\u73b0\u5728\u6bcf\u5f53\u6211\u8bf4\u6cd5\u8bed\u65f6, \u6211\u4f1a\u7acb\u5373\u89c9\u5bdf\u5230\u6211\u72af\u4e86\u8bb8\u591a\u9519\u8bef, \u800c\u6211\u5374\u5f88\u96be\u8868\u8fbe\u81ea\u5df1\u3002\u867d\u7136\u6211\u4ece\u6765\u6ca1\u5b66\u8fc7\u82f1\u8bed, \u751a\u81f3\u4f1a\u72af\u6bd4\u8bb2\u6cd5\u8bed\u66f4\u591a\u7684\u9519\u8bef, \u4f46\u5bf9\u82f1\u6587\u6211\u89c9\u5f97\u6709\u66f4\u591a\u7684\u4fe1\u5fc3\u3002 (\u4f17\u7b11!)
\n\u5218<\/strong>: \u8fd9\u8bdd\u771f\u6709\u610f\u601d\u3002
\nG<\/strong>: \u6211\u5fc5\u987b\u8bf4\u5c31\u8bed\u8a00\u800c\u8a00\u7f8e\u56fd\u4eba\u662f\u975e\u5e38\u4f1a\u5305\u5bb9\u7684, \u800c\u6cd5\u56fd\u4eba\u5c31\u4e0d\u662f\u90a3\u4e48\u5305\u5bb9\u7684\u3002
\n\u5218<\/strong>: \u65f6\u95f4\u4e0d\u591a\u4e86, \u6211\u60f3\u95ee\u6700\u540e\u4e00\u4e2a\u95ee\u9898\u3002\u4ec0\u4e48\u662f\u4f60\u5bf9\u51c6\u5907\u5b66\u6570\u5b66\u7684\u5e74\u8f7b\u5b66\u5b50\u7684\u5efa\u8a00\u5462?
\n\u9648<\/strong>: \u6216\u8bb8\u8bf7\u7ed9\u4e00\u4e9b\u5fe0\u544a, \u6709\u5173\u5e74\u8f7b\u4eba\u5e94\u8be5\u5c3d\u53ef\u80fd\u591a\u5b66\u4e0d\u540c\u7684\u65b9\u5411\u4ee5\u589e\u5e7f\u89c6\u91ce\u6216\u8005\u8be5\u5c3d\u65e9\u4e13\u653b\u4e00\u95e8\u5b66\u95ee\u3002
\nG<\/strong>: \u7ed9\u5efa\u8a00\u603b\u662f\u5f88\u96be\u7684\u3002\u5982\u679c\u4f60\u4e13\u7814\u4e00\u95e8\u5b66\u95ee, \u597d\u5904\u662f\u80fd\u591f\u505a\u5f97\u6108\u6765\u6108\u6df1\u5165, \u4f46\u8fd9\u4e5f\u8bb8\u662f\u975e\u5e38\u5371\u9669\u7684\u4e8b\u3002\u53e6\u4e00\u65b9\u9762, \u5e74\u8f7b\u65f6\u4e00\u4e2a\u4eba\u53ef\u4ee5\u5b66\u4f1a\u5f88\u591a\u4e8b, \u5e74\u7eaa\u6108\u5927\u5c31\u6108\u6765\u6108\u96be\u53bb\u5b66\u65b0\u7684\u4e8b\u7269, \u867d\u7136\u7ecf\u9a8c\u4f1a\u6709\u4e9b\u5e2e\u52a9\u3002\u73b0\u5728\u7531\u4e8e\u7ade\u4e89\u6fc0\u70c8, \u4eba\u4eec\u4e3a\u4e86\u5f88\u5feb\u5730\u53d1\u8868\u8bba\u6587, \u5fc5\u987b\u5f88\u65e9\u5c31\u505a\u4e13\u4e1a\u7684\u7814\u7a76, \u800c\u5b66\u4e60\u96be\u514d\u5360\u53bb\u4e00\u4e9b\u505a\u8bba\u6587\u7684\u65f6\u95f4\u3002\u6211\u8ba4\u4e3a\u5e74\u8f7b\u7684\u5b66\u5b50\u5e94\u8be5\u5b66\u7740\u4e24\u8005\u517c\u987e\u3002\u5f53\u7136\u6709\u4eba\u80fd\u591f\u5b66\u5f88\u5feb, \u4e5f\u6709\u80fd\u591f\u5b66\u5f97\u53c8\u591a\u53c8\u5feb\u975e\u5e38\u4f18\u79c0\u7684\u5b66\u751f, \u4e0d\u8fc7\u4e5f\u6709\u50cf\u6211\u8fd9\u6837\u9700\u8981\u65f6\u95f4\u53bb\u5b66\u4e60\u7684\u5b66\u751f\u3002
\n\u9648<\/strong>: \u6240\u4ee5, \u6839\u636e\u7ecf\u9a8c, \u6bcf\u4e2a\u4eba\u80fd\u591f\u51b3\u5b9a\u81ea\u5df1\u6700\u597d\u7684\u5b66\u4e60\u65b9\u5f0f\u3002\u4f46\u662f, \u8fd9\u5f88\u8d39\u65f6\u95f4\u3002
\nG<\/strong>: \u662f\u554a, \u5f88\u4e0d\u5e78\u5730\u3002\u6ca1\u6709\u89c4\u5219\u662f\u4f60\u53ef\u4ee5\u7167\u7740\u53bb\u505a\u800c\u80fd\u5f97\u5230\u80af\u5b9a\u7684\u7ed3\u679c\u7684, \u4e00\u5207\u90fd\u5f52\u7ed3\u4e8e\u4e2a\u4eba\u5728\u751f\u547d\u4e2d\u62e5\u6709\u7684\u7ecf\u9a8c\u3002
\n\u5218<\/strong>: \u6216\u8bb8\u6211\u4eec\u5fc5\u987b\u5728\u6b64\u6253\u4f4f\u3002\u975e\u5e38\u8c22\u8c22\u4f60, \u8fd9\u771f\u662f\u4e00\u6b21\u975e\u5e38\u6709\u8da3\u7684\u8bbf\u8c08\u3002
\n\u2014\u672c\u6587\u8bbf\u8c08\u8005\u5218\u4e30\u54f2\u4e3a\u4e2d\u592e\u7814\u7a76\u9662\u6570\u5b66\u6240\u7814\u7a76\u5458, \u9648\u6021\u5168\u4e3a\u535a\u58eb\u540e\u7814\u7a76\u751f\u2014<\/p>\n

\u5982\u679c\u4f60\u5bf9\u67d0\u4e2a\u6570\u5b66\u5bb6\u611f\u5174\u8da3, \u53ef\u4ee5\u641c\u7d22\u201d\u6709\u670b\u81f3\u8fdc\u65b9\u6765 \u4e13\u8bbf xxx\u201d. \u6b22\u8fce\u6ce8\u518c\u672c\u7ad9\u8d26\u53f7, \u7136\u540e\u5c06\u5176\u5206\u4eab\u7ed9\u66f4\u591a\u7684\u670b\u53cb.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"

\u7b56 \u753b : \u5218\u592a\u5e73 \u8bbf \u8c08 : \u5218\u4e30\u54f2\u3001 \u9648\u6021\u5168 \u65f6\u95f4: \u4e2d\u534e\u6c11\u56fd\u4e5d\u5341\u4e00\u5e74\u516b\u6708\u4e5d …<\/p>\n

\u6709\u670b\u81ea\u8fdc\u65b9\u6765 \u2014\u2014 \u4e13\u8bbf Mariano Giaquinta \u6559\u6388<\/span> \u9605\u8bfb\u66f4\u591a »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[487,136],"class_list":["post-4169","post","type-post","status-publish","format-standard","hentry","category-net","tag-giaquinta","tag-136"],"_links":{"self":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/4169","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4169"}],"version-history":[{"count":0,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/4169\/revisions"}],"wp:attachment":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4169"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}