Stability of the Calder\'on problem in admissible geometries

TL;DR

This paper establishes log log stability estimates for the inverse boundary value problem on admissible Riemannian manifolds, enhancing understanding of the Calderón problem's stability in geometric settings.

Contribution

It provides the first log log type stability estimates for the Calderón problem on admissible geometries, extending prior uniqueness results.

Findings

Proved log log stability estimates for inverse boundary problems

Connected stability results to anisotropic Calderón problem

Extended stability analysis to higher-dimensional admissible manifolds

Abstract

In this paper we prove log log type stability estimates for inverse boundary value problems on admissible Riemannian manifolds of dimension $n \geq 3$. The stability estimates correspond to a couple of uniqueness results by Dos Santos Ferrera, Kenig, Salo and Uhlmann. These inverse problems arise naturally when studying the anisotropic Calder\'on problem.