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.
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
@article{JEMS_2010_12_6_a5,
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},
year = {2010},
volume = {12},
number = {6},
doi = {10.4171/jems/237},
url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/237/}
}
TY - JOUR AU - Peter Topping TI - Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics JO - Journal of the European Mathematical Society PY - 2010 SP - 1429 EP - 1451 VL - 12 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4171/jems/237/ DO - 10.4171/jems/237 ID - JEMS_2010_12_6_a5 ER -
%0 Journal Article %A Peter Topping %T Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics %J Journal of the European Mathematical Society %D 2010 %P 1429-1451 %V 12 %N 6 %U http://geodesic.mathdoc.fr/articles/10.4171/jems/237/ %R 10.4171/jems/237 %F JEMS_2010_12_6_a5
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