A universal bound for the low eigenvalues of Neumann Laplacians on compact domains in a Hadamard manifold
type: Item
instance of: scholarly article
title: A universal bound for the low eigenvalues of Neumann Laplacians on compact domains in a Hadamard manifold
zbMATH Open document ID: 0941.58021
published in: Monatshefte für Mathematik
publication date: 1999-12-19T00:00:00Z
review text: Let \(\Omega\) be a bounded domain with smooth boundary in a simply connected \(n\) dimensional Hadamard manifold \(M\) with Ricci curvature bounded from below, i.e., \(\text{Ric}_M\geq-(n-1)k^2\). Let \(0<\mu_1\leq\mu_1\leq\dots\leq\mu_n\) be the first \(n\) non-trivial eigenvalues of the scalar Laplacian \(\Delta\) with Neumann boundary conditions. The author gives a computable constant \(C(n,\text{vol}(\Omega),k^2)\) so that \(\mu_1^{-1}+\cdots+\mu_n^{-1}\geq C(n,\text{vol}(\Omega),k^2)\).
reviewed by: Peter B. Gilkey
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1367697
zbMATH Keywords: Ricci curvature bounded from below
zbMATH Keywords: spectral geometry
author: Changyu Xia
MaRDI profile type: Publication
full work available at URL: s006050050054
OpenAlex ID: W2039950324
Wikidata QID: Q125947230
DOI: 10.1007/S006050050054
description: scientific article; zbMATH DE number 1367697