An inverse problem for the minimal surface equation

Abstract

We use the method of higher order linearization to study an inverse boundary value problem for the minimal surface equation on a Riemannian manifold , where the metric is conformally Euclidean. In particular we show that with the knowledge of Dirichlet-to-Neumann map associated to the minimal surface equation, one can determine the Taylor series of the conformal factor at up to a multiplicative constant. We show this both in the full data case and in some partial data cases.