Capillary Surfaces in Manifolds with Nonnegative Scalar Curvature and Strictly Mean Convex Boundary
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929497804111872 |
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| author | Wu, Yujie |
| author_facet | Wu, Yujie |
| contents | In this paper we use stable capillary surfaces (analogous to the $μ$-bubble construction) to study manifolds with strictly mean convex boundary and nonnegative scalar curvature. We give an obstruction to filling 2-manifolds by such 3-manifolds based on the Urysohn width. We also obtain a bandwidth estimate and establish other geometric properties of such manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03993 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Capillary Surfaces in Manifolds with Nonnegative Scalar Curvature and Strictly Mean Convex Boundary Wu, Yujie Differential Geometry In this paper we use stable capillary surfaces (analogous to the $μ$-bubble construction) to study manifolds with strictly mean convex boundary and nonnegative scalar curvature. We give an obstruction to filling 2-manifolds by such 3-manifolds based on the Urysohn width. We also obtain a bandwidth estimate and establish other geometric properties of such manifolds. |
| title | Capillary Surfaces in Manifolds with Nonnegative Scalar Curvature and Strictly Mean Convex Boundary |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.03993 |