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

Topping, Peter. "Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics." Journal of the European Mathematical Society 012.6 (2010): 1429-1451. <http://eudml.org/doc/277449>.

@article{Topping2010,
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.},
author = {Topping, Peter},
journal = {Journal of the European Mathematical Society},
keywords = {quasiconformal maps; pseudolocality; initial metric of bounded curvature; complete flow; quasiconformal maps; pseudolocality; initial metric of bounded curvature; complete flow},
language = {eng},
number = {6},
pages = {1429-1451},
publisher = {European Mathematical Society Publishing House},
title = {Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics},
url = {http://eudml.org/doc/277449},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Topping, Peter
TI - Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 6
SP - 1429
EP - 1451
AB - 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.
LA - eng
KW - quasiconformal maps; pseudolocality; initial metric of bounded curvature; complete flow; quasiconformal maps; pseudolocality; initial metric of bounded curvature; complete flow
UR - http://eudml.org/doc/277449
ER -