Asymptotic geometric regularity of CAT(0) spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912922992640000 |
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| author | Nagano, Koichi |
| author_facet | Nagano, Koichi |
| contents | We prove that if an n-dimensional geodesically complete CAT(0) space has Tits boundary sufficiently close to the (n-1)-dimensional standard unit sphere, then it is bi-Lipschiz homeomorphic to the n-dimensional Euclidean space. As an application, we conclude that if an (n-1)-dimensional geodesically complete CAT(1) space is sufficiently close to the (n-1)-dimensional standard unit sphere, then they are bi-Lipschiz homeomorphic to each other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20533 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic geometric regularity of CAT(0) spaces Nagano, Koichi Differential Geometry Metric Geometry 53C20, 53C23 We prove that if an n-dimensional geodesically complete CAT(0) space has Tits boundary sufficiently close to the (n-1)-dimensional standard unit sphere, then it is bi-Lipschiz homeomorphic to the n-dimensional Euclidean space. As an application, we conclude that if an (n-1)-dimensional geodesically complete CAT(1) space is sufficiently close to the (n-1)-dimensional standard unit sphere, then they are bi-Lipschiz homeomorphic to each other. |
| title | Asymptotic geometric regularity of CAT(0) spaces |
| topic | Differential Geometry Metric Geometry 53C20, 53C23 |
| url | https://arxiv.org/abs/2602.20533 |