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arXiv · 2505.08301

Modified Hawking mass and rigidity of three-manifolds with boundary

Jihyeon Lee·Sanghun Lee
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Abstract

In this paper, we prove a rigidity result for three-dimensional Riemannian manifolds with boundary, under the assumption that a free boundary minimal two-disk, which locally maximizes a modified Hawking mass, is embedded in a $3$-dimensional Riemannian manifold with negative scalar curvature and mean convex boundary. First, we establish area estimates for free boundary strictly stable two-disks. Finally, we show that the $3$-dimensional Riemannian manifold with boundary is locally isometric to the half anti-de Sitter-Schwarzschild manifold.

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Jihyeon Lee, Sanghun Lee. 2025-05-13. Modified Hawking mass and rigidity of three-manifolds with boundary. https://arxiv.org/abs/2505.08301

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