Fractional anisotropic Calderón problem on closed Riemannian manifolds

By Ali Feizmohammadi, Tuhin Ghosh, Katya Krupchyk, Gunther Uhlmann. Journal of differential geometry, 2021

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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.

Subfields: Mathematical Physics, Mechanics of Materials, Modeling and Simulation

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