Spectral determination of analytic bi-axisymmetric plane domains

Let ${\cal D}$ denote the class of bounded simply connected real analytic plane domains with the symmetry of an ellipse. We announce a proof that under generic assumptions, if $\Omega_1, \Omega_2 \in {\cal D}$ and if the Dirichlet spectra coincide, $Spec(\Omega_1) = Spec(\Omega_2)$, then $\Omega_1 = \Omega_2$ up to rigid motion.

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Published 1 January 1999