Isospectral convex domains in Euclidean space
type: Item
instance of: scholarly article
title: Isospectral convex domains in Euclidean space
zbMATH Open document ID: 0840.58046
author: Carolyn S. Gordon
author: David L. Webb
published in: Mathematical Research Letters
publication date: 1995-11-16T00:00:00Z
review text: The authors deal with the question whether the eigenvalue spectrum of the Laplace operator on a domain in the Euclidean plane determines the domain up to congruence. H. Urakawa constructed examples of isospectral domains in \(\mathbb{R}^n\) \((n\geq 4)\). Thus far, all examples of noncongruent isospectral domains in Euclidean space are nonconvex. Thus the following question has remained open: are there pairs of convex domains in Euclidean space which are isospectral but not congruent? In this paper, the authors have shown that one can modify slightly Urakawa's constructon to obtain a pair of convex domains in Euclidean \(n\)-space for \(n\geq 4\) which are noncongruent yet isospectral for both Dirichlet and Neumann boundary conditions. The proof of Neumann isospectrality uses very recent results of Hubert Pesce.
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 817722
zbMATH Keywords: isospectral convex domains in \(\mathbb{R}^ n\) \((n\geq 4)\)
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: Neumann boundary conditions
reviewed by: Stana Nikčević
MaRDI profile type: Publication
full work available at URL: mrl.1994.v1.n5.a2
OpenAlex ID: W1966517154
DOI: 10.4310/MRL.1994.V1.N5.A2
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description: scientific article; zbMATH DE number 817722