Preprint
Oct 2026
On the planar Neumann--Poincar\'e inverse spectral problem
Does the Neumann--Poincar\'e spectrum determine a planar domain up to an extended M\"obius transformation? We construct a pair showing that the answer is no, even for analytic, strictly convex, algebraic boundaries. Their operators are similar. We then prove a positive result for prescribed finite-dimensional families...
Habib Ammari, Matthew J. Colbrook
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