Modified Hawking mass and rigidity of three-manifolds with boundary
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915287041835008 |
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| author | Lee, Jihyeon Lee, Sanghun |
| author_facet | Lee, Jihyeon Lee, Sanghun |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_08301 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modified Hawking mass and rigidity of three-manifolds with boundary Lee, Jihyeon Lee, Sanghun Differential Geometry 53C25, 53C24, 53C21 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. |
| title | Modified Hawking mass and rigidity of three-manifolds with boundary |
| topic | Differential Geometry 53C25, 53C24, 53C21 |
| url | https://arxiv.org/abs/2505.08301 |