Work

Fractional Calderón problem with a potential

Year: 2026

Type: preprint

Abstract: We prove that the knowledge of local Cauchy data for a fractional Schrödinger equation on a smooth closed and connected Riemannian manifold of dimension at least two determines the manifold, its metric, and a smooth complex- valued potential, up to an isometry fixing the observation set. The observation set may be any nonempty open subset and no further geometric assumptions are required. The proof uses functional calculus identities to recover the local action of the resolvent of the Laplace-Beltrami operator.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.06766

Authors: Feizmohammadi, Ali, Krupchyk, Katya, Uhlmann, Gunther

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Anisotropic Inverse Problems: Nonlocality, Nonlinearity, and High Frequencies

OpenAlex ID: W7220673754

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