Inverse conductivity problem on a Riemann surface

We present an application of the Faddeev-Henkin exponential ansatz and of the d-to-d-bar map on the boundary to inverse conductivity problem on a bordered Riemann surface in CP2. In our approach we use integral formulas for operator d-bar developed in [HP1]-[HP4] and integral formulas for holomorphic functions on Riemann surfaces from [P].