Coincidence of length spectra does not imply isospectrality
Spectral Theory
2009-11-11 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
Penrose--Lifshits mushrooms are planar domains coming in nonisometric pairs with the same geodesic length spectrum. Recently S. Zelditch raised the question whether such billiards also have the same eigenvalue spectrum for the Dirichlet Laplacian (conjecturing ``no''). Here we show that generically (in the class of smooth domains) the two members of a mushroom pair have different spectra.
Keywords
Cite
@article{arxiv.math/0505200,
title = {Coincidence of length spectra does not imply isospectrality},
author = {S. A. Fulling and Peter Kuchment},
journal= {arXiv preprint arXiv:math/0505200},
year = {2009}
}
Comments
8 pages, 5 figures