Noncritical maps on geodesically complete spaces with curvature bounded above
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
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| _version_ | 1866929645448855552 |
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| author | Fujioka, Tadashi |
| author_facet | Fujioka, Tadashi |
| contents | We define and study the regularity of distance maps on geodesically complete spaces with curvature bounded above. We prove that such a regular map is locally a Hurewicz fibration. This regularity can be regarded as a dual concept of Perelman's regularity in the geometry of Alexandrov spaces with curvature bounded below. As a corollary we obtain a sphere theorem for geodesically complete CAT(1) spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_08859 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Noncritical maps on geodesically complete spaces with curvature bounded above Fujioka, Tadashi Differential Geometry Metric Geometry 53C20, 53C21, 53C23 We define and study the regularity of distance maps on geodesically complete spaces with curvature bounded above. We prove that such a regular map is locally a Hurewicz fibration. This regularity can be regarded as a dual concept of Perelman's regularity in the geometry of Alexandrov spaces with curvature bounded below. As a corollary we obtain a sphere theorem for geodesically complete CAT(1) spaces. |
| title | Noncritical maps on geodesically complete spaces with curvature bounded above |
| topic | Differential Geometry Metric Geometry 53C20, 53C21, 53C23 |
| url | https://arxiv.org/abs/2107.08859 |