Limits of manifolds with boundary II
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909569947533312 |
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| author | Yamaguchi, Takao Zhang, Zhilang |
| author_facet | Yamaguchi, Takao Zhang, Zhilang |
| contents | In this paper, as a continuation of [30], we consider the Gromov-Hausdorff convergence and collapsing in the family of compact Riemannian manifolds with boundary satisfying lower bounds on the sectional curvatures of interior manifolds, boundaries and the second fundamental forms of boundaries, and an upper diameter bound. We describe the local geometric structure of the limit spaces, and establish some stability results including Lipschitz homotopy stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limits of manifolds with boundary II Yamaguchi, Takao Zhang, Zhilang Differential Geometry 53C20 In this paper, as a continuation of [30], we consider the Gromov-Hausdorff convergence and collapsing in the family of compact Riemannian manifolds with boundary satisfying lower bounds on the sectional curvatures of interior manifolds, boundaries and the second fundamental forms of boundaries, and an upper diameter bound. We describe the local geometric structure of the limit spaces, and establish some stability results including Lipschitz homotopy stability. |
| title | Limits of manifolds with boundary II |
| topic | Differential Geometry 53C20 |
| url | https://arxiv.org/abs/2504.05497 |