Eigenfunction asymptotics and spectral rigidity of the ellipse

Hamid Hezari, Steve Zelditch

Research output: Contribution to journalArticlepeer-review


Microlocal defect measures for Cauchy data of Dirichlet, resp. Neumann, eigenfunctions of an ellipse E are determined. We prove that, for any invariant curve for the billiard map on the boundary phase space B*E of an ellipse, there exists a sequence of eigenfunctions whose Cauchy data concentrates on the invariant curve. We use this result to give a new proof that ellipses are infinitesimally spectrally rigid among C1 domains with the symmetries of the ellipse.

Original languageEnglish (US)
Pages (from-to)23-52
Number of pages30
JournalJournal of Spectral Theory
Issue number1
StatePublished - 2022


  • Cauchy data
  • Laplacian
  • Spectral rigidity
  • billiards
  • ellipse

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology


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