One can hear the corners of a drum

Abstract

We prove that the presence or absence of corners is spectrally determined in the following sense: any simply connected domain with piecewise smooth Lipschitz boundary cannot be isospectral to any connected domain, of any genus, which has smooth boundary. Moreover, we prove that amongst all domains with Lipschitz, piecewise smooth boundary and fixed genus, the presence or absence of corners is uniquely determined by the spectrum. This means that corners are an elementary geometric spectral invariant; one can hear corners.

arXiv commentThis is the author's original manuscript that was submitted to Bulletin of the London Mathematical Society. A significantly revised final version is published in BLMS

References in corpus (1)

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