PIC1 pinched manifolds are flat or compact
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866911538303991808 |
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| author | Deruelle, Alix Lee, Man-Chun Schulze, Felix Simon, Miles Topping, Peter M. |
| author_facet | Deruelle, Alix Lee, Man-Chun Schulze, Felix Simon, Miles Topping, Peter M. |
| contents | Hamilton's pinching conjecture, that three-dimensional complete non-compact manifolds with pinched Ricci curvature are flat, has recently been resolved using Ricci flow. In this paper we prove a direct analogue of that result in all dimensions. In order to do so we develop a lifting technique that allows us to handle manifolds that are collapsed at infinity. This new method also gives an alternative way of handling collapsed manifolds in the known three-dimensional case. As part of this approach, we prove a Ricci flow curvature estimate of a type that would normally be derived from the Harnack inequality, but without requiring the strong curvature positivity hypothesis demanded by Harnack. We give an improved gap theorem as a further application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22086 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PIC1 pinched manifolds are flat or compact Deruelle, Alix Lee, Man-Chun Schulze, Felix Simon, Miles Topping, Peter M. Differential Geometry 53E20, 53C20 Hamilton's pinching conjecture, that three-dimensional complete non-compact manifolds with pinched Ricci curvature are flat, has recently been resolved using Ricci flow. In this paper we prove a direct analogue of that result in all dimensions. In order to do so we develop a lifting technique that allows us to handle manifolds that are collapsed at infinity. This new method also gives an alternative way of handling collapsed manifolds in the known three-dimensional case. As part of this approach, we prove a Ricci flow curvature estimate of a type that would normally be derived from the Harnack inequality, but without requiring the strong curvature positivity hypothesis demanded by Harnack. We give an improved gap theorem as a further application. |
| title | PIC1 pinched manifolds are flat or compact |
| topic | Differential Geometry 53E20, 53C20 |
| url | https://arxiv.org/abs/2603.22086 |