Calderon inverse Problem for the Schrodinger Operator on Riemann Surfaces

Abstract

On a fixed smooth compact Riemann surface with boundary $(M_0,g)$, we show that the Cauchy data space (or Dirichlet-to-Neumann map $\mc{N}$) of the Schrödinger operator $\Delta +V$ with $V\in C^2(M_0)$ determines uniquely the potential $V$. We also discuss briefly the corresponding consequences for potential scattering at 0 frequency on Riemann surfaces with asymptotically Euclidean or asymptotically hyperbolic ends.

16 pages

References in corpus (2)

• Global uniqueness from partial Cauchy data in two dimensions
• Partial Data for the Calderon Problem in Two Dimensions