Spectral properties of constant mean curvature submanifolds in hyperbolic space
type: Item
instance of: scholarly article
title: Spectral properties of constant mean curvature submanifolds in hyperbolic space
zbMATH Open document ID: 0948.58004
DOI: 10.1023/A:1006690108504
author: Philippe Castillon
published in: Annals of Global Analysis and Geometry
publication date: 2000-11-22T00:00:00Z
review text: The author studies the essential spectrum of the Laplacian \(\Delta\) and of the stability operator \(S\) on hypersurfaces with constant mean curvature in hyperbolic space. He proves the following: Theorem. Let \(i: M^n\hookrightarrow H^{n+1}\) be an immersion with constant mean curvature \(h<1\). If the total curvature is finite, then \[ \sigma_{\text{ess}}(\Delta)\in \Biggl[{(n- 1)^2\over 4}(1- h^2),+\infty\Biggr) \quad\text{and} \quad\sigma_{\text{ess}}(S)\in \Biggl[{(n+ 1)^2\over 4} (1- h^2),+\infty\Biggr). \]
Mathematics Subject Classification ID: 58C40
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1396331
zbMATH Keywords: essential spectrum
zbMATH Keywords: Laplacian
zbMATH Keywords: hypersurfaces with constant mean curvature
zbMATH Keywords: hyperbolic space
MaRDI profile type: Publication
full work available at URL: a:1006690108504
OpenAlex ID: W34553146
description: scientific article; zbMATH DE number 1396331