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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

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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:
DateEvent
2010Published
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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