The anisotropic Calder\'on problem for high fixed frequency

TL;DR

This paper proves that on certain curved manifolds, the Dirichlet-to-Neumann map at high fixed frequency uniquely determines the potential in Schrödinger operators, advancing inverse boundary value problem understanding.

Contribution

It establishes uniqueness results for the anisotropic Calderón problem at high fixed frequency on non-positively curved manifolds.

Findings

Unique determination of potential from Dirichlet-to-Neumann map

Results apply to simply connected compact manifolds with convex boundaries

Advances inverse problems in geometric analysis

Abstract

We consider Schr\"odinger operators at a fixed high frequency on simply connected compact Riemannian manifolds with non-positive sectional curvatures and smooth strictly convex boundaries. We prove that the Dirichlet-to-Neumann map uniquely determines the potential.