Geodesic
Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics
Journal of the European Mathematical Society, Tome 12 (2010) no. 6, pp. 1429-1451.

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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.
DOI : 10.4171/jems/237
Classification : 58-XX, 00-XX
Keywords: 
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     author = {Peter Topping},
     title = {Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics},
     journal = {Journal of the European Mathematical Society},
     pages = {1429--1451},
     publisher = {mathdoc},
     volume = {12},
     number = {6},
     year = {2010},
     doi = {10.4171/jems/237},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/237/}
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Peter Topping. Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics. Journal of the European Mathematical Society, Tome 12 (2010) no. 6, pp. 1429-1451. doi : 10.4171/jems/237. http://geodesic.mathdoc.fr/articles/10.4171/jems/237/

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