Remarks on the anisotropic Calder\'{o}n problem

TL;DR

This paper establishes uniqueness and convexity results for the anisotropic Calderón problem on Riemannian manifolds and explores inverse problems related to semilinear elliptic equations.

Contribution

It provides new uniqueness theorems for the anisotropic Calderón problem and extends convexity and inverse problem results to general Riemannian manifolds.

Findings

Uniqueness results for the anisotropic Calderón problem on transversally anisotropic manifolds

Convexity of the Dirichlet-to-Neumann map range near zero potential

Results on Calderón type inverse problems for semilinear elliptic equations

Abstract

We show uniqueness results for the anisotropic Calder\'{o}n problem stated on transversally anisotropic manifolds. Moreover, we give a convexity result for the range of Dirichlet-to-Neumann maps on general Riemannian manifolds near the zero potential. Finally, we present results for Calder\'{o}n type inverse problems associated to semilinear elliptic equations on general Riemannian manifolds.