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Sharp decay estimates for the logarithmic fast diffusion equation and the Ricci flow on surfaces
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Topping, Peter and Yin, Hao (2017) Sharp decay estimates for the logarithmic fast diffusion equation and the Ricci flow on surfaces. Annals of PDE, 3 . 6. doi:10.1007/s40818-017-0024-x ISSN 2199-2576.
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Official URL: http://doi.org/10.1007/s40818-017-0024-x
Abstract
We prove the sharp local L^1 - L^\infty smoothing estimate for the logarithmic fast diffusion equation, or equivalently, for the Ricci flow on surfaces. Our estimate almost instantly implies an improvement of the known L^p - L^\infty estimate for p larger than 1. It also has several applications in geometry, providing the missing step in order to pose the Ricci flow with rough initial data in the noncompact case, for example starting with a general noncompact Alexandrov surface, and giving the sharp asymptotics for the contracting cusp Ricci flow, as we show elsewhere.
| 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, Differential equations, Partial | ||||||||
| Journal or Publication Title: | Annals of PDE | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 2199-2576 | ||||||||
| Official Date: | June 2017 | ||||||||
| Dates: |
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| Volume: | 3 | ||||||||
| Number of Pages: | 16 | ||||||||
| Article Number: | 6 | ||||||||
| DOI: | 10.1007/s40818-017-0024-x | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 2 November 2016 | ||||||||
| Date of first compliant Open Access: | 25 May 2017 | ||||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC) | ||||||||
| Grant number: | Grant No. EP/K00865X/1 (EPSRC), 11471300 (NSFC) |
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