Resonances and balls in obstacle scattering with Neumann boundary conditions

Abstract

We consider scattering by an obstacle in $\Real^d$, $d\ge 3$ odd. We show that for the Neumann Laplacian if an obstacle has the same resonances as the ball of radius $\rho$ does, then the obstacle is a ball of radius $\rho$. We give related results for obstacles which are disjoint unions of several balls of the same radius.