Radius estimates for nearly stable H-hypersurfaces of dimension 2, 3, and 4
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915091682689024 |
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| author | Tinaglia, Giuseppe Zhou, Alex |
| author_facet | Tinaglia, Giuseppe Zhou, Alex |
| contents | In this paper we study the geometry of complete constant mean curvature (CMC) hypersurfaces immersed in an (n + 1)-dimensional Riemannian manifold N (n = 2, 3 and 4) with sectional curvatures uniformly bounded from below. We generalise radius estimates given by Rosenberg [32] (n = 2) and by Elbert, Nelli and Rosenberg [13] and Cheng [2] (n = 3, 4) to nearly stable CMC hypersurfaces immersed in N. We also prove that certain CMC hypersurfaces effectively embedded in N must be proper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02151 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Radius estimates for nearly stable H-hypersurfaces of dimension 2, 3, and 4 Tinaglia, Giuseppe Zhou, Alex Differential Geometry 53A10 In this paper we study the geometry of complete constant mean curvature (CMC) hypersurfaces immersed in an (n + 1)-dimensional Riemannian manifold N (n = 2, 3 and 4) with sectional curvatures uniformly bounded from below. We generalise radius estimates given by Rosenberg [32] (n = 2) and by Elbert, Nelli and Rosenberg [13] and Cheng [2] (n = 3, 4) to nearly stable CMC hypersurfaces immersed in N. We also prove that certain CMC hypersurfaces effectively embedded in N must be proper. |
| title | Radius estimates for nearly stable H-hypersurfaces of dimension 2, 3, and 4 |
| topic | Differential Geometry 53A10 |
| url | https://arxiv.org/abs/2411.02151 |