Robin spectral rigidity of strictly convex domains with a reflectional symmetry

2016/09/05 by Hamid Hezari, Hezari, Hamid
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.AP #math.SP

paper · pdf · doi:10.48550/arxiv.1609.01011

14 pages

arxiv created 2016/09/05 · openalex publication_date 2016/09/05 · arxiv updated 2016/09/06 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

This is a note on a recent paper of De Simoi-Kaloshin-Wei \citeDKW. We show that using their results combined with wave trace invariants of Guillemin-Melrose and the heat trace invariants of Zayed for the Laplacian with Robin boundary conditions, one can extend the Dirichlet/Neumann spectral rigidity results of \citeDKW to the case of Robin boundary conditions. We will consider the same generic subset as in \citeDKW of smooth strictly convex \mathbb Z₂-symmetric planar domains sufficiently close to a circle, however we pair them with arbitrary \mathbb Z₂-symmetric smooth Robin functions on the boundary and of course allow deformations of Robin functions as well.

Citations

• The propagation of singularities along gliding rays
• Can One Hear the Shape of a Drum?

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