A Sharp Upper Bound for the First Eigenvalue of the Laplacian of Compact Hypersurfaces in Rank-1 Symmetric Spaces

Proceedings Mathematical Sciences

G Santhanum¹ 

[1] Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 0 0, India$$

关键词: Hypersurface;    center-of-mass;    rank-1 symmetric space;    Laplacian;    eigenvalue.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝑀 be a closed hypersurface in a simply connected rank-1 symmetric space $overline{M}$. In this paper, we give an upper bound for the first eigenvalue of the Laplacian of 𝑀 in terms of the Ricci curvature of $overline{M}$ and the square of the length of the second fundamental form of the geodesic spheres with center at the center-of-mass of 𝑀.

【 授权许可】

Unknown