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On the regularity of Ricci flows coming out of metric spaces
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Deruelle, Alix, Schulze, Felix and Simon, Miles (2021) On the regularity of Ricci flows coming out of metric spaces. Journal of the European Mathematical Society, 24 (7). pp. 2233-2277. doi:10.4171/JEMS/1138 ISSN 1435-9855.
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WRAP-On-regularity-Ricci-flows-coming-metric-spaces-Schulze-2020.pdf - Accepted Version - Requires a PDF viewer. Download (648Kb) | Preview |
Official URL: http://doi.org/10.4171/JEMS/1138
Abstract
We consider smooth, not necessarily complete, Ricci flows, (M,g(t))t∈(0,T) with Ric(g(t))≥−1 and |Rm(g(t))|≤c/t for all t∈(0,T) coming out of metric spaces (M,d0) in the sense that (M,d(g(t)),x0)→(M,d0,x0) as t↘0 in the pointed Gromov-Hausdorff sense. In the case that Bg(t)(x0,1)⋐M for all t∈(0,T) and d0 is generated by a smooth Riemannian metric in distance coordinates, we show using Ricci-harmonic map heat flow, that there is a corresponding smooth solution g~(t)t∈(0,T) to the δ-Ricci-DeTurck flow on an Euclidean ball Br(p0)⊂Rn, which can be extended to a smooth solution defined for t∈[0,T). We further show, that this implies that the original solution g can be extended to a smooth solution on Bd0(x0,r/2) for t∈[0,T), in view of the method of Hamilton.
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, Global differential geometry, Riemannian manifolds | ||||||||||||
Journal or Publication Title: | Journal of the European Mathematical Society | ||||||||||||
Publisher: | European Mathematical Society Publishing House | ||||||||||||
ISSN: | 1435-9855 | ||||||||||||
Official Date: | 18 October 2021 | ||||||||||||
Dates: |
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Volume: | 24 | ||||||||||||
Number: | 7 | ||||||||||||
Page Range: | pp. 2233-2277 | ||||||||||||
DOI: | 10.4171/JEMS/1138 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Copyright Holders: | Copyright © EMS 2020 | ||||||||||||
Date of first compliant deposit: | 19 June 2020 | ||||||||||||
Date of first compliant Open Access: | 19 June 2020 | ||||||||||||
RIOXX Funder/Project Grant: |
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