Scalar-mean rigidity theorem for compact manifolds with boundary
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910858936844288 |
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| author | Wang, Jinmin Wang, Zhichao Zhu, Bo |
| author_facet | Wang, Jinmin Wang, Zhichao Zhu, Bo |
| contents | We prove a scalar-mean rigidity theorem for compact Riemannian manifolds with boundary in dimension less than five by developing a dimension reduction argument for mean curvature, which extends Schoen-Yau's dimension reduction argument for scalar curvature. As a corollary, we prove the sharp spherical radius rigidity theorem and best NNSC fill-in in terms of the mean curvature. Moreover, we prove a Lipschitz Listing type scalar-mean rigidity theorem for these dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalar-mean rigidity theorem for compact manifolds with boundary Wang, Jinmin Wang, Zhichao Zhu, Bo Differential Geometry We prove a scalar-mean rigidity theorem for compact Riemannian manifolds with boundary in dimension less than five by developing a dimension reduction argument for mean curvature, which extends Schoen-Yau's dimension reduction argument for scalar curvature. As a corollary, we prove the sharp spherical radius rigidity theorem and best NNSC fill-in in terms of the mean curvature. Moreover, we prove a Lipschitz Listing type scalar-mean rigidity theorem for these dimensions. |
| title | Scalar-mean rigidity theorem for compact manifolds with boundary |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2409.14503 |