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Pyramid Ricci flow in higher dimensions
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Mcleod, Andrew Donald and Topping, Peter (2020) Pyramid Ricci flow in higher dimensions. Mathematische Zeitschrift, 296 . pp. 511-523. doi:10.1007/s00209-020-02472-1 ISSN 0025-5874.
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Official URL: https://doi.org/10.1007/s00209-020-02472-1
Abstract
In this paper, we construct a pyramid Ricci flow starting with a complete Riemannian manifold (Mn ; g0) that is PIC1, or more generally satisfies a lower curvature bound KIC1 . 0.
That is, instead of constructing a flow on M [0; T ], we construct it on a subset of space-time that a union of parabolic cylinders Bg0(x0; k) [0; Tk] for each k 2 N, where Tk # 0, and prove estimates on the curvature and Riemannian distance. More generally, we construct a pyramid Ricci flow starting with any noncollapsed IC1-limit space, and use it to establish that such limit spaces are globally homeomorphic to smooth manifolds via homeomorphisms that are locally bi-H¨ older.
| 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: | Mathematische Zeitschrift | |||||||||
| Publisher: | Springer | |||||||||
| ISSN: | 0025-5874 | |||||||||
| Official Date: | October 2020 | |||||||||
| Dates: |
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| Volume: | 296 | |||||||||
| Page Range: | pp. 511-523 | |||||||||
| DOI: | 10.1007/s00209-020-02472-1 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 24 October 2019 | |||||||||
| Date of first compliant Open Access: | 3 February 2020 | |||||||||
| RIOXX Funder/Project Grant: |
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