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Fractional anisotropic Calder\'on problem on closed Riemannian manifolds

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arxiv 2112.03480 v1 pith:J5AFPYWJ submitted 2021-12-07 math.AP

classification math.AP
keywords riemannianclosedanisotropiccalderfractionalmanifoldsproblemdimensions
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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

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stability of Gel'fand's inverse interior spectral problem for Schr\"odinger operators

    math.AP 2025-07 conditional novelty 7.0 of 10

    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.

  2. Anisotropic Calder\'{o}n problem of a nearly Laplace-Beltrami operator of order $2+$

    math.AP 2025-06 reject novelty 5.0 of 10

    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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