Compactness of isospectral compact manifolds with bounded curvatures
type: Item
instance of: scholarly article
title: Compactness of isospectral compact manifolds with bounded curvatures
zbMATH Open document ID: 0885.58092
author: Gengqiang Zhou
published in: Pacific Journal of Mathematics
publication date: 1996-12-15T00:00:00Z
full work available at URL: v181no1.html
review text: Suppose that \({\mathfrak J}^n (C)\) is the class of all Riemannian metrics on a given \(n\)-dimensional closed manifold such that their associated Laplacians (on functions) have the same spectrum by counting multiplicities and their sectional curvatures are uniformly bounded,\dots, by a constant \(C>0\). We show that the isospectral class \({\mathfrak J}^n (C)\) is compact in the \(C^\infty\)-topology. This generalizes our previous \(C^\infty\)-compactness result, which holds for dimensions up to seven.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 950186
zbMATH Keywords: isospectral manifolds
zbMATH Keywords: compactness
zbMATH Keywords: curvature bounds
zbMATH Keywords: Riemannian metrics
zbMATH Keywords: Laplacians
reviewed by: Guodong Zhou
MaRDI profile type: Publication
OpenAlex ID: W2163574206
Wikidata QID: Q125864873
DOI: 10.2140/PJM.1997.181.187
description: scientific article; zbMATH DE number 950186