Geometry of three-dimensional manifolds with positive scalar curvature
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913376469254144 |
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| author | Munteanu, Ovidiu Wang, Jiaping |
| author_facet | Munteanu, Ovidiu Wang, Jiaping |
| contents | The purpose of this paper is to derive volume and other geometric information for three-dimensional complete manifolds with positive scalar curvature. In the case that the Ricci curvature is nonnegative, it is shown that the volume of the manifold must be of linear growth when the scalar curvature is bounded from below by a positive constant. This answers a question of Gromov in the affirmative for dimension three. Volume growth estimates are also obtained for the case when scalar curvature decays to zero. In fact, results of similar nature are established for the more general case that the Ricci curvature is asymptotically nonnegative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_05595 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Geometry of three-dimensional manifolds with positive scalar curvature Munteanu, Ovidiu Wang, Jiaping Differential Geometry Analysis of PDEs The purpose of this paper is to derive volume and other geometric information for three-dimensional complete manifolds with positive scalar curvature. In the case that the Ricci curvature is nonnegative, it is shown that the volume of the manifold must be of linear growth when the scalar curvature is bounded from below by a positive constant. This answers a question of Gromov in the affirmative for dimension three. Volume growth estimates are also obtained for the case when scalar curvature decays to zero. In fact, results of similar nature are established for the more general case that the Ricci curvature is asymptotically nonnegative. |
| title | Geometry of three-dimensional manifolds with positive scalar curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2201.05595 |