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arXiv · 2309.01333

Rigidity of free boundary minimal disks in mean convex three-manifolds

Rondinelle Batista·Barnabé Lima·João Silva
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Abstract

The purpose of this article is study rigidity of free boundary minimal two-disks that locally maximize the modified Hawking mass on a Riemannian three-manifold with positive lower bound on its scalar curvature and mean convex boundary. Assuming the strict stability of {\Sigma}, we prove that a neighborhood of it in M is isometric to one of the half de Sitter-Schwarzschild space.

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Rondinelle Batista, Barnabé Lima, João Silva. 2023-09-04. Rigidity of free boundary minimal disks in mean convex three-manifolds. https://arxiv.org/abs/2309.01333

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