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Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics
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Topping, Peter (2010) Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics. Journal of the European Mathematical Society, Vol.12 (No.6). pp. 1429-1451. doi:10.4171/JEMS/237 ISSN 1435-9855.
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Official URL: http://dx.doi.org/10.4171/JEMS/237
Abstract
By exploiting Perelman's pseudolocality theorem, we prove a new compactness theorem for Ricci flows. By optimising the theory in the two-dimensional case, and invoking the theory of quasiconformal maps, we establish a new existence theorem which generates a Ricci flow starting at an arbitrary incomplete metric, with Gauss curvature bounded above, on an arbitrary surface. The criterion we assert for well-posedness is that the flow should be complete for all positive times; our discussion of uniqueness also invokes pseudolocality.
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, Metric spaces | ||||
Journal or Publication Title: | Journal of the European Mathematical Society | ||||
Publisher: | European Mathematical Society Publishing House | ||||
ISSN: | 1435-9855 | ||||
Official Date: | 2010 | ||||
Dates: |
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Volume: | Vol.12 | ||||
Number: | No.6 | ||||
Page Range: | pp. 1429-1451 | ||||
DOI: | 10.4171/JEMS/237 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), Leverhulme Trust (LT) |
Data sourced from Thomson Reuters' Web of Knowledge
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