Rigidity of homogeneous Lam\'e systems

Abstract

In this short paper, we show that any Lam\'e system whose Dirichlet-to-Neumann map for the elastic wave equation agrees with the one arising from the homogeneous Lam\'e system must actually be homogeneous. We do not need to impose any assumptions for the Lam\'e coefficients that we aim to recover. We use the fact that the homogeneous system gives rise to a geometry that is both simple and admits a strictly convex foliation.