Inverse Conductivity Problem on Riemann Surfaces

An electrical potential U on a bordered Riemann surface X with conductivity function σ >0 satisfies equation d ( σ d c U )=0. The problem of effective reconstruction of σ from electrical currents measurements (Dirichlet-to-Neumann mapping) on the boundary: U | bX ↦ σ d c U | bX is studied. We extend to the case of Riemann surfaces the reconstruction scheme given, firstly, by R. Novikov (Funkc. Anal. Ego Priloz. 22:11–22, 2008 ) for simply connected X . We apply for this new kernels for on the affine algebraic Riemann surfaces constructed in Henkin ( arXiv:0804.3761 , 2008 ).