Fractional anisotropic Calder\'on problem on closed Riemannian manifolds
Analysis of PDEs
2025-09-10 v1
Abstract
In this paper we solve the fractional anisotropic Calder\'on problem on closed Riemannian manifolds of dimensions two and higher. Specifically, we prove that the knowledge of the local source-to-solution map for the fractional Laplacian, given on an arbitrary small open nonempty a priori known subset of a smooth closed connected Riemannian manifold, determines the Riemannian manifold up to an isometry. This can be viewed as a nonlocal analog of the anisotropic Calder\'on problem in the setting of closed Riemannian manifolds, which is wide open in dimensions three and higher.
Keywords
Cite
@article{arxiv.2112.03480,
title = {Fractional anisotropic Calder\'on problem on closed Riemannian manifolds},
author = {Ali Feizmohammadi and Tuhin Ghosh and Katya Krupchyk and Gunther Uhlmann},
journal= {arXiv preprint arXiv:2112.03480},
year = {2025}
}