Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics

Peter Topping
2010 Journal of the European Mathematical Society (Print)  
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 wellposedness is that the flow should be complete for all positive times; our discussion of uniqueness also invokes pseudolocality. *
doi:10.4171/jems/237 fatcat:3vzor5zq5nfqvdbhehcxtyan2e