An inverse problem for the Riemannian minimal surface equation

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

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