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

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) over cap circle plus e). Here g<^> is a simple Riemannian metric on Rn-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 similar to g agree, then the Taylor series of the conformal factor c similar to at x(n) = 0 is equal to a positive constant. We also show a partial data result when n = 3. ; peerReviewed