An inverse problem for the Riemannian minimal surface equation

Abstract: In this paper we consider determining a minimal surface embedded in a Riemannian manifold $\Sigma\times \mathbb{R}$. We show that if $\Sigma$ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated Dirichlet-to-Neumann map for the minimal surface equation determine $\Sigma$ up to an isometry.