Report
Recovering a Riemannian manifold from minimal surface areas
| Title: | Recovering a Riemannian manifold from minimal surface areas |
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| Authors: | Carstea, Catalin, Lassas, Matti, Liimatainen, Tony, Tzou, Leo |
| Publication Year: | 2026 |
| Collection: | Mathematical Physics |
| Subject Terms: | Differential Geometry, Mathematical Physics, Analysis of PDEs |
| Description: | 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 $\(π_1(M,\partial M)=0\)$ and a non-trapping condition. The Einstein result includes the AI was used to streamline and verify some of the proofs |
| Document Type: | Working Paper |
| DOI: | 10.48550/arXiv.2610.13405 |
| Access URL: | https://arxiv.org/abs/2610.13405 |
| Accession Number: | edsarx.2610.13405 |
| Database: | arXiv |
| DOI: | 10.48550/arXiv.2610.13405 |
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