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Local control on the geometry in 3D Ricci flow
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Simon, Miles and Topping, Peter (2022) Local control on the geometry in 3D Ricci flow. Journal of Differential Geometry, 122 (3). pp. 467-518. doi:10.4310/jdg/1675712996 ISSN 0022-040X.
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Official URL: https://doi.org/10.4310/jdg/1675712996
Abstract
The geometry of a ball within a Riemannian manifold is coarsely controlled if it has a lower bound on its Ricci curvature and a positive lower bound on its volume. We prove that such coarse local geometric control must persist for a definite amount of time under three-dimensional Ricci flow, and leads to local C/t decay of the full curvature tensor, irrespective of what is happening beyond the local region. As a by-product, our results generalise the Pseudolocality theorem of Perelman and Tian-Wang in this dimension by not requiring the Ricci curvature to be almost-positive, and not asking the volume growth to be almost-Euclidean.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Ricci flow, Riemannian manifolds | ||||||||
| Journal or Publication Title: | Journal of Differential Geometry | ||||||||
| Publisher: | Lehigh University | ||||||||
| ISSN: | 0022-040X | ||||||||
| Official Date: | November 2022 | ||||||||
| Dates: |
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| Volume: | 122 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | pp. 467-518 | ||||||||
| DOI: | 10.4310/jdg/1675712996 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 2 September 2020 | ||||||||
| Date of first compliant Open Access: | 3 September 2020 | ||||||||
| RIOXX Funder/Project Grant: |
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