Sharp upper bound for the first eigenvalue

Binoy; G. Santhanam

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arXiv · 1208.1669

Sharp upper bound for the first eigenvalue

Binoy·G. Santhanam

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Abstract

Let $M$ be a closed hypersurface in a noncompact rank-1 symmetric space $(\bar{\mathbb{M}}, ds^2)$ with $-4 \leq K_{\bar{\mathbb{M}}} \leq -1,$ or in a complete, simply connected Riemannian manifold $\mathbb{M}$ such that $0 \leq K_{\mathbb{M}} \leq δ^2$ or $K_{\mathbb{M}} \leq k$ where $k = -δ^2$ or 0. In this paper we give sharp upperbounds for the first eigenvalue of laplacian of $M$.

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BibTeX RIS

Binoy, G. Santhanam. 2013-01-05. Sharp upper bound for the first eigenvalue. https://arxiv.org/abs/1208.1669

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