First eigenvalue pinching for Euclidean hypersurfaces via \(k\) -th mean curvatures
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- 作者：Yingxiang Hu ; Hongwei Xu ; Entao Zhao
- 关键词：First eigenvalue ; differentiable pinching theorem ; Euclidean hypersurfaces ; $$k$$ k ; th mean curvature ; 53C20 ; 53C40 ; 58C40
- 刊名：Annals of Global Analysis and Geometry
- 出版年：2015
- 出版时间：June 2015
- 年：2015
- 卷：48
- 期：1
- 页码：23-35
- 全文大小：442 KB
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Hongwei Xu (1)
Entao Zhao (1)
1. Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, People鈥檚 Republic of China - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Analysis
Statistics for Business, Economics, Mathematical Finance and Insurance
Mathematical and Computational Physics
Group Theory and Generalizations
Geometry - 出版者：Springer Netherlands
- ISSN：1572-9060
文摘
In this article, we prove pinching theorems for the first eigenvalue \(\lambda _1(M)\) of the Laplacian on compact Euclidean hypersurfaces involving the integrals of \(k\)-th mean curvature. Particularly, we show that under a suitable pinching condition, the hypersurface is starshaped and almost-isometric to a standard sphere. Based on our theorems, we prove some pinching results for the almost-Einstein and almost-umbilical hypersurfaces in Euclidean space.