Abstract
ABSTRACTThis is a note on a paper of De Simoi–Kaloshin–Wei. We show that by combining their techniques with the 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 De Simoi–Kaloshin–Wei to the case of Robin boundary conditions. We will consider the same generic subset as did by De Simoi–Kaloshin–Wei of smooth strictly convex ℤ2-symmetric planar domains sufficiently close to a circle, however we pair them with arbitrary ℤ2-symmetric smooth Robin functions on the boundary and of course allow deformations of Robin functions as well.
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