{"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 $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> is the square norm of the second fundamental form.</jats:p>","PeriodicalId":0,"journal":{"name":"","volume":"27 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"FIRST EIGENVALUE CHARACTERISATION OF CLIFFORD HYPERSURFACES AND VERONESE SURFACES\",\"authors\":\"PEIYI WU\",\"doi\":\"10.1017/s0004972724000273\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n\\t <jats:p>We give a sharp estimate for the first eigenvalue of the Schrödinger operator <jats:inline-formula>\\n\\t <jats:alternatives>\\n\\t\\t<jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0004972724000273_inline1.png\\\"/>\\n\\t\\t<jats:tex-math>\\n$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\":0,\"journal\":{\"name\":\"\",\"volume\":\"27 3\",\"pages\":\"\"},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0004972724000273\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0004972724000273","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","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.