Calderon inverse Problem with partial data on Riemann Surfaces

Abstract

On a fixed smooth compact Riemann surface with boundary $(M_0,g)$, we show that for the Schrödinger operator $\Delta +V$ with potential $V\in C^{1,\alpha }(M_0)$ for some $\alpha >0$, the Dirichlet-to-Neumann map $N{|}_{\Gamma }$ measured on an open set $\Gamma \subset \partial M_0$ 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.

27 pages. Corrections and modifications in the Complex Geometric Optics solutions; regularity assumption strenghtened to $C^{1,\alpha }$

References in corpus (3)

• Limiting Carleman weights and anisotropic inverse problems
• Global uniqueness from partial Cauchy data in two dimensions
• Calderon inverse Problem for the Schrodinger Operator on Riemann Surfaces

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