Resonances and balls in obstacle scattering with Neumann boundary conditions
The goal of this note is to show that for obstacle scattering in \(\mathbb{R}^N\), \(N\geq 3\) odd, a ball is uniquely determined by its resonance for the Laplacian with Neumann boundary conditions. The author actually shows a somewhat stronger result: If \({\mathcal O}_1\) and \({\mathcal O}_2\) have the same (Neumann) resonances and \({\mathcal O}_1\) is the disjoint union of \(m\) balls, each of radius \(\rho\), then so is \({\mathcal O}_2\).
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