The spectral geometry of flat disks
type: Item
instance of: scholarly article
title: The spectral geometry of flat disks
zbMATH Open document ID: 0712.58012
DOI: 10.1215/S0012-7094-90-06106-X
author: Robert Brooks
author: Curtis T. McMullen
author: Yakov Eliashberg
published in: Duke Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: Flat disks \(D_ 1\) and \(D_ 2\) are said to be isometric (resp. piecewise isometric) near the boundary if there are neighborhoods \(N_ 1\) and \(N_ 2\) of \(\partial D_ 1\) and \(\partial D_ 2\) such that \(N_ 1\) is isometric to \(N_ 2\) (resp. \(N_ 1\) can be subdivided into finitely many pieces and rearranged to obtain \(N_ 2)\). The authors show that there exist compact flat disks (resp. planar disks) \(D_ 1\) and \(D_ 2\) which are isometric (resp. piecewise isometric) near the boundary, but which are not isospectral for either Dirichlet or Neumann boundary conditions.
Mathematics Subject Classification ID: 58C40
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 4171976
zbMATH Keywords: spectral geometry
zbMATH Keywords: heat equation
zbMATH Keywords: flat disks
zbMATH Keywords: planar disks
zbMATH Keywords: Dirichlet or Neumann boundary conditions
reviewed by: Dušan Repovš
MaRDI profile type: Publication
cites work: The First Eigenvalue of a Scalene Triangle
cites work: Q3344779
cites work: Q5614192
cites work: Can One Hear the Shape of a Drum?
cites work: Extensions of Normal Immersions of S 1 into R 2
cites work: Compact isospectral sets of surfaces
cites work: A note on Hayman's theorem on the bass note of a drum
cites work: Q3482489
full work available at URL: s0012-7094-90-06106-x
OpenAlex ID: W2130586730
description: scientific article; zbMATH DE number 4171976