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\"\"<\/figure>\n\n\n\n

\u3010\u74b0\u7403\u65b0\u805e\u5831\u8a0a\u3011\u6fb3\u9580\u5927\u5b78\u79d1\u6280\u5b78\u9662\u8b1b\u5ea7\u6559\u6388\u517c\u6578\u5b78\u7cfb\u7cfb\u4e3b\u4efb\u6842\u9577\u5cf0\u7684\u7a81\u7834\u6027\u7814\u7a76\u8ad6\u6587\u300a\u4e09\u89d2\u5f62\u4e0a\u7b2c\u4e8cNeumann\u7279\u5fb5\u51fd\u6578\u81e8\u754c\u9ede\u7684\u552f\u4e00\u6027\u300b\uff08Uniqueness of critical points of the second Neumann eigenfunctions on triangles\uff09\u65bc\u9802\u5c16\u6578\u5b78\u671f\u520a\u300a\u6578\u5b78\u65b0\u9032\u5c55\u300b\uff08Inventiones mathematicae\uff09\u767c\u8868\u3002\u9019\u662f\u9996\u6b21\u6709\u6fb3\u9580\u5b78\u8005\u5728\u6578\u5b78\u56db\u5927\u9802\u7d1a\u671f\u520a\u767c\u8868\u7814\u7a76\u6210\u679c\uff0c\u5f70\u986f\u4e86\u6fb3\u5927\u6578\u5b78\u7cfb\u5728\u5b78\u8853\u754c\u7684\u6838\u5fc3\u7af6\u722d\u529b\u8207\u5f71\u97ff\u529b\u3002<\/p>\n\n\n\n

\"\"
\u25b2\u6fb3\u9580\u5927\u5b78\u79d1\u6280\u5b78\u9662\u8b1b\u5ea7\u6559\u6388\u517c\u6578\u5b78\u7cfb\u7cfb\u4e3b\u4efb\u6842\u9577\u5cf0<\/figcaption><\/figure>\n\n\n\n

\u8a72\u7814\u7a76\u805a\u7126\u65bc\u7f8e\u570b\u6578\u5b78\u5bb6Jeffrey Rauch\u65bc1974\u5e74\u63d0\u51fa\u7684\u201c\u71b1\u9ede\u731c\u60f3\u201d\uff0c\u901a\u904e\u7269\u7406\u73fe\u8c61\u4f86\u7406\u89e3\u9019\u4e00\u6578\u5b78\u554f\u984c\u7684\u6838\u5fc3\uff0c\u5728\u4e00\u9593\u7d55\u71b1\u7684\u623f\u9593\u5167\uff0c\u5c40\u90e8\u71b1\u6e90\u7522\u751f\u7684\u71b1\u91cf\u64f4\u6563\u904e\u7a0b\u4e2d\u6703\u51fa\u73fe\u6eab\u5ea6\u7684\u6975\u503c\u9ede\u3002\u6309\u7167\u76f4\u89ba\uff0c\u9019\u4e9b\u6eab\u5ea6\u6975\u503c\u61c9\u50c5\u51fa\u73fe\u5728\u623f\u9593\u7684\u908a\u754c\uff0c\u800c\u975e\u5167\u90e8\u3002\u9019\u4e00\u7269\u7406\u76f4\u89ba\u5728\u5e36\u6709Neumann\uff08\u7d55\u71b1\uff09\u908a\u754c\u689d\u4ef6\u7684\u71b1\u65b9\u7a0b\u6846\u67b6\u4e0b\uff0c\u88ab\u8f49\u5316\u70ba\u56b4\u8b39\u7684\u6578\u5b78\u8868\u8ff0\u3002\u5f9e\u6578\u5b78\u5c64\u9762\u800c\u8a00\uff0c\u201c\u71b1\u9ede\u731c\u60f3\u201d\u7684\u5177\u9ad4\u65b7\u8a00\u70ba\uff1a\u5728\u5e73\u9762\u51f8\u5340\u57df\u4e2d\uff0c\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u7684\u7b2c\u4e8cNeumann\u7279\u5fb5\u51fd\u6578\uff08\u5373\u4e3b\u5c0e\u6eab\u5ea6\u5411\u5747\u52fb\u72c0\u614b\u8870\u6e1b\u7684\u6700\u6162\u6a21\u5f0f\uff09\uff0c\u5176\u6700\u5927\u503c\u8207\u6700\u5c0f\u503c\u50c5\u5b58\u5728\u65bc\u5340\u57df\u7684\u908a\u754c\u8655\u3002\u534a\u500b\u591a\u4e16\u7d00\u4ee5\u4f86\uff0c\u9019\u4e00\u554f\u984c\u53d7\u5230\u4e86\u773e\u591a\u570b\u969b\u9802\u5c16\u6578\u5b78\u5bb6\u7684\u95dc\u6ce8\uff0c\u5305\u62ec\u83f2\u723e\u8332\u734e\u5f97\u4e3b\u9676\u54f2\u8ed2\uff08Terence Tao\uff09\u3001Wendelin Werner\uff0c\u4ee5\u53ca\u570b\u969b\u6578\u5b78\u5bb6\u5927\u6703\uff08ICM\uff09\u5831\u544a\u4ebaRichard F. Bass\u3001David Jerison\u3001Nikolai Nadirashvili \u7b49\u3002\u5b78\u754c\u570d\u7e5e\u4e0d\u540c\u5e7e\u4f55\u5340\u57df\u548c\u5404\u985e\u7279\u6b8a\u60c5\u5f62\u5c55\u958b\u7814\u7a76\uff0c\u53d6\u5f97\u4e86\u4e00\u7cfb\u5217\u91cd\u8981\u9032\u5c55\uff0c\u4f46\u5e73\u9762\u4e09\u89d2\u5f62\u9019\u4e00\u6700\u7c21\u55ae\u7684\u51f8\u591a\u908a\u5f62\uff0c\u537b\u9577\u671f\u6210\u70ba\u7814\u7a76\u96e3\u984c\u3002<\/p>\n\n\n\n

\"\"
\u25b2\u71b1\u9ede\u731c\u60f3<\/figcaption><\/figure>\n\n\n\n

\u7814\u7a76\u5718\u968a\u5c07\u7814\u7a76\u91cd\u9ede\u653e\u5728\u4e09\u89d2\u5f62\u60c5\u5f62\u4e0a\uff0c\u958b\u5c55\u4e86\u7cfb\u7d71\u4e14\u6df1\u5165\u7684\u5206\u6790\u5de5\u4f5c\uff0c\u53d6\u5f97\u4e86\u591a\u9805\u95dc\u9375\u6210\u679c\uff1a\u4e00\u662f\u89e3\u6c7a\u4e86\u9676\u54f2\u8ed2\u65bc2012\u5e74\u5728 Polymath Project 7\u4e2d\u63d0\u51fa\u7684\u201c\u7b2c\u4e8cNeumann\u7279\u5fb5\u51fd\u6578\u6700\u5927\u503c\u7cbe\u78ba\u4f4d\u7f6e\u201d\u7684\u516c\u958b\u554f\u984c\uff1b\u4e8c\u662f\u5b8c\u5584\u4e26\u5b8c\u6574\u89e3\u6c7a\u4e86Judge\u548cMondal\u65bc2020\u5e74\u5728\u300a\u6578\u5b78\u5e74\u520a\u300b\uff08Annals of Mathematics\uff09\u63d0\u51fa\u7684\u908a\u754c\u81e8\u754c\u9ede\u731c\u60f3\uff1b\u4e09\u662f\u5c0dDavid Jerison\u63d0\u51fa\u7684\u7279\u5fb5\u51fd\u6578\u55ae\u8abf\u6027\u76f8\u95dc\u7591\u554f\u7d66\u51fa\u4e86\u80af\u5b9a\u7b54\u6848\uff1b\u6b64\u5916\uff0c\u9084\u91dd\u5c0d\u96f6\u9ede\u96c6\u7684\u5206\u4f48\u3001\u6df7\u5408\u908a\u754c\u7279\u5fb5\u503c\u4e0d\u7b49\u5f0f\u7b49\u591a\u500b\u516c\u958b\u554f\u984c\uff0c\u63d0\u4f9b\u4e86\u660e\u78ba\u7684\u80af\u5b9a\u89e3\u7b54\u3002\u9019\u4e9b\u7814\u7a76\u7d50\u679c\u901a\u904e\u5275\u65b0\u7684\u5c0d\u7a31\u8ad6\u8b49\u65b9\u6cd5\u548c\u7279\u5fb5\u503c\u754c\u9650\u5206\u6790\u5f97\u4ee5\u56b4\u683c\u78ba\u7acb\uff0c\u4e0d\u50c5\u6df1\u5165\u5256\u6790\u4e86\u4e09\u89d2\u5f62\u4e2d\u7b2c\u4e8cNeumann\u7279\u5fb5\u51fd\u6578\u7684\u76f8\u95dc\u6027\u8cea\uff0c\u5176\u63d0\u51fa\u7684\u7814\u7a76\u65b9\u6cd5\u8207\u6240\u5f97\u7d50\u8ad6\uff0c\u4e5f\u70ba\u8b5c\u5e7e\u4f55\u3001\u504f\u5fae\u5206\u65b9\u7a0b\u7b49\u76f8\u95dc\u6578\u5b78\u9818\u57df\u7684\u7814\u7a76\u63d0\u4f9b\u4e86\u57fa\u790e\u5de5\u5177\u8207\u53c3\u8003\u601d\u8def\u3002<\/p>\n\n\n\n

\u662f\u6b21\u6210\u679c\u7684\u767c\u8868\u4e0d\u50c5\u662f\u5c0d\u6fb3\u5927\u79d1\u7814\u5be6\u529b\u7684\u91cd\u8981\u80af\u5b9a\uff0c\u4e5f\u70ba\u6fb3\u5927\u6578\u5b78\u5b78\u79d1\u9032\u4e00\u6b65\u6df1\u8015\u570b\u969b\u524d\u6cbf\u7814\u7a76\u53ca\u62d3\u5c55\u5168\u7403\u5b78\u8853\u5408\u4f5c\u7db2\u7d61\u5960\u5b9a\u5805\u5be6\u57fa\u790e\u3002\u8a72\u8ad6\u6587\u662f\u6842\u9577\u5cf0\u806f\u540c\u83ef\u5357\u7406\u5de5\u5927\u5b78\u6578\u5b78\u5b78\u9662\u526f\u6559\u6388\u59da\u82e5\u98db\u3001\u897f\u5b89\u4ea4\u901a\u5927\u5b78\u6578\u5b78\u8207\u7d71\u8a08\u5b78\u9662\u6559\u6388\u9673\u7d05\u658c\u5408\u8457\u3002\u5168\u6587\u53ef\u700f\u89bd\uff1ahttps:\/\/link.springer.com\/article\/10.1007\/s00222-025-01398-x<\/u><\/a>\u3002<\/p>\n\n\n\n

\u300a\u6578\u5b78\u65b0\u9032\u5c55\u300b\uff08Inventiones Mathematicae\uff09\u8207\u300a\u6578\u5b78\u5b78\u5831\u300b\uff08Acta Mathematica\uff09\u3001\u300a\u6578\u5b78\u5e74\u520a\u300b\uff08Annals of Mathematics\uff09\u3001\u300a\u7f8e\u570b\u6578\u5b78\u6703\u96dc\u8a8c\u300b\uff08Journal of the American Mathematical Society\uff09\u4e26\u7a31\u6578\u5b78\u9818\u57df\u7684\u56db\u5927\u9802\u7d1a\u671f\u520a\uff0c\u662f\u8861\u91cf\u570b\u969b\u6578\u5b78\u7814\u7a76\u6700\u9ad8\u5b78\u8853\u6c34\u5e73\u7684\u91cd\u8981\u6a19\u6746\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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