Convergence of Riemannian 2-manifolds under a uniform curvature and contractibility bound
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913644062703616 |
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| author | Dott, Tobias |
| author_facet | Dott, Tobias |
| contents | We consider uniformly semi-locally 1-connected sequences of closed connected Riemannian 2-manifolds. In particular, we assume that the manifolds are homeomorphic to each other and that their total absolute curvature is uniformly bounded. The purpose of this paper is a description of the Gromov-Hausdorff limits of such sequences. Our work extends earlier investigations by Burago and Shioya. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_06351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of Riemannian 2-manifolds under a uniform curvature and contractibility bound Dott, Tobias Metric Geometry Differential Geometry 51F99, 53C20, 53C45 (Primary) 54F15 (Secondary) We consider uniformly semi-locally 1-connected sequences of closed connected Riemannian 2-manifolds. In particular, we assume that the manifolds are homeomorphic to each other and that their total absolute curvature is uniformly bounded. The purpose of this paper is a description of the Gromov-Hausdorff limits of such sequences. Our work extends earlier investigations by Burago and Shioya. |
| title | Convergence of Riemannian 2-manifolds under a uniform curvature and contractibility bound |
| topic | Metric Geometry Differential Geometry 51F99, 53C20, 53C45 (Primary) 54F15 (Secondary) |
| url | https://arxiv.org/abs/2501.06351 |