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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
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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 | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of 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) |
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