Calderon inverse Problem for the Schrodinger Operator on Riemann Surfaces

Details Calderon inverse Problem for the Schrodinger Operator on Riemann Surfaces Calderon inverse Problem for the Schrodinger Operator on Riemann Surfaces

2009-04-24

arxiv.org/abs/0904.3804v1

Mathematics

Differential Geometry

16 pages

Scientific paper

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 Schr\"odinger 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.

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