Estimates for the first eigenvalue of Jacobi operator on hypersurfaces with constant mean curvature in spheres

Daguang Chen; Qing-Ming Cheng

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arXiv · 1610.00374

Estimates for the first eigenvalue of Jacobi operator on hypersurfaces with constant mean curvature in spheres

Daguang Chen·Qing-Ming Cheng

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Abstract

In this paper, we study the first eigenvalue of Jacobi operator on an $n$-dimensional non-totally umbilical compact hypersurface with constant mean curvature $H$ in the unit sphere $S^{n+1}(1)$. We give an optimal upper bound for the first eigenvalue of Jacobi operator, which only depends on the mean curvature $H$ and the dimension $n$.

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BibTeX RIS

Daguang Chen, Qing-Ming Cheng. 2016-10-03. Estimates for the first eigenvalue of Jacobi operator on hypersurfaces with constant mean curvature in spheres. https://arxiv.org/abs/1610.00374

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