Calderon inverse Problem for the Schrodinger Operator on Riemann Surfaces

2009/04/24 by Colin Guillarmou, Guillarmou, Colin, Leo Tzou +1
Mathematics · #35R30 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:35R30

paper · pdf · doi:10.48550/arxiv.0904.3804

16 pages

arxiv created 2009/04/24 · arxiv updated 2009/12/01

Abstract

On a fixed smooth compact Riemann surface with boundary (M₀,g), we show that the Cauchy data space (or Dirichlet-to-Neumann map \mcN) of the Schrödinger operator Δ+V with V∈ C²(M₀) 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.

Related

• The anisotropic Calderón problem for high fixed frequency
• The Calderón problem in the L^p framework on Riemann surfaces
• The Calderón problem is an inverse source problem
• The Calderón problem with partial data
• Determining an unbounded potential from Cauchy data in admissible geometries