$C^{\infty }$ spectral rigidity of the ellipse

Abstract

We prove that ellipses are infinitesimally spectrally rigid among $C^{\infty }$ domains with the symmetries of the ellipse.

This is a major revision which gives full details on the Hadamard variation of the wave trace on a domain with boundary

References in corpus (1)

• Quantum ergodic restriction theorems, II: manifolds without boundary

Cited by in corpus (2)

• Critical partitions and nodal deficiency of billiard eigenfunctions
• Inverse problems in spectral geometry