Spectral determination of semi-regular polygons

Alberto Enciso; Javier Gómez-Serrano

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arXiv · 1709.05960

Spectral determination of semi-regular polygons

Alberto Enciso·Javier Gómez-Serrano

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Abstract

Let us say that an $n$-sided polygon is semi-regular if it is circumscriptible and its angles are all equal but possibly one, which is then larger than the rest. Regular polygons, in particular, are semi-regular. We prove that semi-regular polygons are spectrally determined in the class of convex piecewise smooth domains. Specifically, we show that if $\Omega$ is a convex piecewise smooth planar domain, possibly with straight corners, whose Dirichlet or Neumann spectrum coincides with that of an $n$-sided semi-regular polygon $P_n$, then $\Omega$ is congruent to $P_n$.

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Alberto Enciso, Javier Gómez-Serrano. 2017-09-18. Spectral determination of semi-regular polygons. https://arxiv.org/abs/1709.05960

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