{"title":"clifford 超曲面和 veronese 曲面的第一特征值表征","authors":"PEIYI WU","doi":"10.1017/s0004972724000273","DOIUrl":null,"url":null,"abstract":"\n\t <jats:p>We give a sharp estimate for the first eigenvalue of the Schrödinger operator <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972724000273_inline1.png\"/>\n\t\t<jats:tex-math>\n$L:=-\\Delta -\\sigma $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> which is defined on the closed minimal submanifold <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972724000273_inline2.png\"/>\n\t\t<jats:tex-math>\n$M^{n}$\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> in the unit sphere <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972724000273_inline3.png\"/>\n\t\t<jats:tex-math>\n$\\mathbb {S}^{n+m}$\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula>, where <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972724000273_inline4.png\"/>\n\t\t<jats:tex-math>\n$\\sigma $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> is the square norm of the second fundamental form.</jats:p>","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"FIRST EIGENVALUE CHARACTERISATION OF CLIFFORD HYPERSURFACES AND VERONESE SURFACES\",\"authors\":\"PEIYI WU\",\"doi\":\"10.1017/s0004972724000273\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n\\t <jats:p>We give a sharp estimate for the first eigenvalue of the Schrödinger operator <jats:inline-formula>\\n\\t <jats:alternatives>\\n\\t\\t<jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0004972724000273_inline1.png\\\"/>\\n\\t\\t<jats:tex-math>\\n$L:=-\\\\Delta -\\\\sigma $\\n</jats:tex-math>\\n\\t </jats:alternatives>\\n\\t </jats:inline-formula> which is defined on the closed minimal submanifold <jats:inline-formula>\\n\\t <jats:alternatives>\\n\\t\\t<jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0004972724000273_inline2.png\\\"/>\\n\\t\\t<jats:tex-math>\\n$M^{n}$\\n</jats:tex-math>\\n\\t </jats:alternatives>\\n\\t </jats:inline-formula> in the unit sphere <jats:inline-formula>\\n\\t <jats:alternatives>\\n\\t\\t<jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0004972724000273_inline3.png\\\"/>\\n\\t\\t<jats:tex-math>\\n$\\\\mathbb {S}^{n+m}$\\n</jats:tex-math>\\n\\t </jats:alternatives>\\n\\t </jats:inline-formula>, where <jats:inline-formula>\\n\\t <jats:alternatives>\\n\\t\\t<jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0004972724000273_inline4.png\\\"/>\\n\\t\\t<jats:tex-math>\\n$\\\\sigma $\\n</jats:tex-math>\\n\\t </jats:alternatives>\\n\\t </jats:inline-formula> is the square norm of the second fundamental form.</jats:p>\",\"PeriodicalId\":50720,\"journal\":{\"name\":\"Bulletin of the Australian Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Australian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0004972724000273\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Australian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0004972724000273","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
FIRST EIGENVALUE CHARACTERISATION OF CLIFFORD HYPERSURFACES AND VERONESE SURFACES
We give a sharp estimate for the first eigenvalue of the Schrödinger operator
$L:=-\Delta -\sigma $
which is defined on the closed minimal submanifold
$M^{n}$
in the unit sphere
$\mathbb {S}^{n+m}$
, where
$\sigma $
is the square norm of the second fundamental form.
期刊介绍：
Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way.
Published Bi-monthly
Published for the Australian Mathematical Society
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