An inverse problem for the minimal surface equation

We use the method of higher order linearization to study an inverse boundary value problem for minimal surface equation on a Riemannian manifold $(\mathbb{R}^n,g)$, where metric $g$ is conformally Euclidean. In particular we show that with knowledge Dirichlet-to-Neumann map associated equation, one can determine Taylor series conformal factor $c(x)$ at $x_n=0$ up multiplicative constant. this both in full data case and some partial cases.