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arXiv · 2112.03480

Fractional anisotropic Calder\'on problem on closed Riemannian manifolds

Ali Feizmohammadi·Tuhin Ghosh·Katya Krupchyk·Gunther Uhlmann
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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.

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Ali Feizmohammadi, Tuhin Ghosh, Katya Krupchyk, Gunther Uhlmann. 2021-12-07. Fractional anisotropic Calder\'on problem on closed Riemannian manifolds. https://doi.org/10.4310/jdg/1757353909

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