Quasianalyticity and geometric rigidity in anisotropic Calderón's problem

@misc{chen2026quasianalyticity,
  title = {{Quasianalyticity and geometric rigidity in anisotropic Calderón's problem}},
  author = {Lu Chen and Yan Jiang and Hongyu Liu and Longyue Tao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.15813},
  eprint = {2608.15813},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.15813},
}

TY  - UNPB
TI  - Quasianalyticity and geometric rigidity in anisotropic Calderón's problem
AU  - Lu Chen
AU  - Yan Jiang
AU  - Hongyu Liu
AU  - Longyue Tao
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2608.15813
UR  - https://arxiv.org/abs/2608.15813
AB  - The anisotropic Calderón problem of determining a smooth Riemannian metric from boundary measurements, up to a boundary-fixing diffeomorphism, remains open in dimensions n≥3~\cite{uhlmann2009electrical}. We establish unique identifiability results in two complementary regimes. In the first, the identity principle for quasianalytic functions propagates boundary information and yields unique identifiability on compact manifolds without a prescribed product structure, including a partial-data consequence; under a prescribed normal geometry, quasianalyticity is needed only in the distinguished direction. In the second, suitable symmetry or one-sided ordering assumptions lead to unique identifiability at C^∞ regularity with full or restricted boundary access. Taken together, the results exhibit a tradeoff among regularity, geometric structure, and boundary access: quasianalyticity supplies continuation when no global product structure is prescribed, while symmetry or one-sided order replaces that continuation at C^∞ regularity.
ER  -