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Recovering a Riemannian manifold from minimal surface areas

  • Catalin Carstea
  • Matti Lassas
  • Tony Liimatainen
  • Leo Tzou
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Abstract

We study the recovery of a three-dimensional Riemannian manifold from the areas of minimal surfaces. We show that areas of minimal surfaces determine the metric on manifolds foliated by minimal surfaces, up to boundary-fixing isometry. This resolves the conjecture on boundary rigidity for least-area data in an exterior formulation, even without topological restrictions on the minimal surfaces. We also prove global rigidity for Einstein metrics on compact three-manifolds with boundary, assuming (π1(M,∂ M)=0) and a non-trapping condition. The Einstein result includes the

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Cite

BibTeXRIS
BibTeX
@misc{carstea2026recovering,
  title = {{Recovering a Riemannian manifold from minimal surface areas}},
  author = {Catalin Carstea and Matti Lassas and Tony Liimatainen and Leo Tzou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13405},
  eprint = {2610.13405},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13405},
}
RIS
TY  - UNPB
TI  - Recovering a Riemannian manifold from minimal surface areas
AU  - Catalin Carstea
AU  - Matti Lassas
AU  - Tony Liimatainen
AU  - Leo Tzou
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.13405
UR  - https://arxiv.org/abs/2610.13405
AB  - We study the recovery of a three-dimensional Riemannian manifold from the areas of minimal surfaces. We show that areas of minimal surfaces determine the metric on manifolds foliated by minimal surfaces, up to boundary-fixing isometry. This resolves the conjecture on boundary rigidity for least-area data in an exterior formulation, even without topological restrictions on the minimal surfaces. We also prove global rigidity for Einstein metrics on compact three-manifolds with boundary, assuming (π_1(M,∂ M)=0) and a non-trapping condition. The Einstein result includes the
ER  -