An inverse problem for the minimal surface equation in the presence of a riemannian metric

Abstract In this work we study an inverse problem for the minimal surface equation on a Riemannian manifold (R n, g) where the metric is of the form g (x) = c (x) (g ^ ⊕ e). Here g ^ is a simple Riemannian metric on R n − 1, e is the Euclidean metric on R and c a smooth positive function. We show that if the associated Dirichlet-to-Neumann maps corresponding to metrics g and c ~ g agree, then the Taylor series of the conformal factor c ~ at x n = 0 is equal to a positive constant. We also show a partial data result when n = 3.