Work

The conformal Poisson embedding method for the anisotropic Calderón problem with a potential

Year: 2026

Type: preprint

Abstract: We prove that the local Dirichlet-to-Neumann map of $Δ_g+q$ determines a compact connected real-analytic Riemannian manifold of dimension at least three and a real-analytic real-valued potential, up to a diffeomorphism fixing the observed boundary and the conformal gauge of the equation. The result is new even when $q$ is constant, i.e. for the fixed-frequency (Helmholtz) equation $Δ_g u+λu=0$. The measurements are restricted to an arbitrary nonempty open boundary set $Γ$. The proof develops conformal Poisson embeddings method and uses coordinates given by quotients of solutions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.13592

Authors: Cârstea, Cătălin I., Liimatainen, Tony, Lin, Yi-Hsuan, Trad, William

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Alexander von Humboldt-Stiftung, Universität Duisburg-Essen, National Science and Technology Council

Award: G6218650241

OpenAlex ID: W7221549637

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