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The conformal Poisson embedding method for the anisotropic Calderón problem with a potential
Abstract
We prove that the local Dirichlet-to-Neumann map of Δg+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 Δg 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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BibTeX
@misc{carstea2026conformal,
title = {{The conformal Poisson embedding method for the anisotropic Calderón problem with a potential}},
author = {Cătălin I. Cârstea and Tony Liimatainen and Yi-Hsuan Lin and William Trad},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13592},
eprint = {2610.13592},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13592},
}
RIS
TY - UNPB
TI - The conformal Poisson embedding method for the anisotropic Calderón problem with a potential
AU - Cătălin I. Cârstea
AU - Tony Liimatainen
AU - Yi-Hsuan Lin
AU - William Trad
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13592
UR - https://arxiv.org/abs/2610.13592
AB - 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.
ER -