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
Cet article a éte moissonné depuis la source EMS Press
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.
@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
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
Cité par Sources :