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arXiv · 2610.13405

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 $\(π_1(M,\partial M)=0\)$ and a non-trapping condition. The Einstein result includes the

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Catalin Carstea, Matti Lassas, Tony Liimatainen, Leo Tzou. 2026-10-09. Recovering a Riemannian manifold from minimal surface areas. https://arxiv.org/abs/2610.13405

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