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arXiv · 2610.13592

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

Cătălin I. Cârstea·Tony Liimatainen·Yi-Hsuan Lin·William Trad
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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.

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Cătălin I. Cârstea, Tony Liimatainen, Yi-Hsuan Lin, William Trad. 2026-10-09. The conformal Poisson embedding method for the anisotropic Calderón problem with a potential. https://arxiv.org/abs/2610.13592

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