clifford 超曲面和 veronese 曲面的第一特征值表征

Pub Date : 2024-04-25 DOI:10.1017/s0004972724000273
PEIYI WU
{"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}
引用次数: 0

摘要

我们给出了薛定谔算子$L:=-\Delta -\sigma $的第一个特征值的尖锐估计值,该算子定义在单位球$\mathbb {S}^{n+m}$ 中的封闭最小子球面$M^{n}$上,其中$\sigma $是第二基本形式的平方规范。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1