English

Sharp upper bound for the first eigenvalue

Differential Geometry 2013-01-08 v3

Abstract

Let MM be a closed hypersurface in a noncompact rank-1 symmetric space (Mˉ,ds2)(\bar{\mathbb{M}}, ds^2) with 4KMˉ1,-4 \leq K_{\bar{\mathbb{M}}} \leq -1, or in a complete, simply connected Riemannian manifold M\mathbb{M} such that 0KMδ20 \leq K_{\mathbb{M}} \leq \delta^2 or KMkK_{\mathbb{M}} \leq k where k=δ2k = -\delta^2 or 0. In this paper we give sharp upperbounds for the first eigenvalue of laplacian of MM.

Keywords

Cite

@article{arxiv.1208.1669,
  title  = {Sharp upper bound for the first eigenvalue},
  author = {Binoy and G. Santhanam},
  journal= {arXiv preprint arXiv:1208.1669},
  year   = {2013}
}
R2 v1 2026-06-21T21:47:54.464Z