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Fractional anisotropic Calder\'on problem on closed Riemannian manifolds
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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.
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Cited by 2 Pith papers
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Stability of Gel'fand's inverse interior spectral problem for Schr\"odinger operators
Approximate eigen-data on an open subset determine a closed Riemannian manifold up to Lipschitz distance epsilon^(1/12) and a Lipschitz potential up to epsilon^(1/(80n)), giving double-logarithmic stability.
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Anisotropic Calder\'{o}n problem of a nearly Laplace-Beltrami operator of order $2+$
The paper claims an anisotropic Calderon uniqueness theorem for a logarithmic Laplacian of order 2+, but the central Paley-Wiener argument is invalid.
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