Work

Recovering a Riemannian manifold from minimal surface areas

Year: 2026

Type: preprint

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

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.13405

Authors: Carstea, Catalin, Lassas, Matti, Liimatainen, Tony, Tzou, Leo

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221555333

Cites:

Cited by:

Related to: 10