PreprintarXiv licencearXiv
Local rigidity of conformally Euclidean metrics for the anisotropic Calderón problem
Abstract
We prove local rigidity of every smooth conformally Euclidean metric for the anisotropic Calderón problem on smooth compact domains M⊂ℝn, n≥3. Any smooth Riemannian metric g sufficiently close to a fixed background g0=e2ce in Hs(M), with integer s>n/2+1, having the same Dirichlet-to-Neumann map satisfies g=Φ*g0 for a smooth diffeomorphism Φ fixing the boundary pointwise.
Related
- Local rigidity of conformally Euclidean metrics for the anisotropic Helmholtz equation at fixed energy
- The anisotropic Calderón problem: rigidity near the Euclidean metric
- The Calderón problem for near-Euclidean metrics
- The anisotropic Calderón problem for Riemannian metrics at high fixed frequency
- Quasianalyticity and geometric rigidity in anisotropic Calderón's problem
BibTeX
@misc{munozthon2026local,
title = {{Local rigidity of conformally Euclidean metrics for the anisotropic Calderón problem}},
author = {Sebastián Muñoz-Thon and Plamen Stefanov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.13400},
eprint = {2609.13400},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13400},
}
RIS
TY - UNPB
TI - Local rigidity of conformally Euclidean metrics for the anisotropic Calderón problem
AU - Sebastián Muñoz-Thon
AU - Plamen Stefanov
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2609.13400
UR - https://arxiv.org/abs/2609.13400
AB - We prove local rigidity of every smooth conformally Euclidean metric for the anisotropic Calderón problem on smooth compact domains M⊂ℝ^n, n≥3. Any smooth Riemannian metric g sufficiently close to a fixed background g_0=e^2ce in H^s(M), with integer s>n/2+1, having the same Dirichlet-to-Neumann map satisfies g=Φ^*g_0 for a smooth diffeomorphism Φ fixing the boundary pointwise.
ER -