Abstract
We prove that ellipses are infinitesimally spectrally rigid among domains with the symmetries of the ellipse.
Citation
Hamid Hezari. Steve Zelditch. "$C^{\infty} $ spectral rigidity of the ellipse." Anal. PDE 5 (5) 1105 - 1132, 2012. https://doi.org/10.2140/apde.2012.5.1105
Information
Received: 4 May 2011; Revised: 11 July 2012; Accepted: 6 August 2012; Published: 2012
First available in Project Euclid: 20 December 2017
zbMATH: 1264.35150
MathSciNet: MR3022850
Digital Object Identifier: 10.2140/apde.2012.5.1105
Subjects:
Primary:
35PXX
Keywords:
ellipses
,
inverse spectral problems
,
isospectral deformations
,
spectral rigidity
Rights: Copyright © 2012 Mathematical Sciences Publishers