How to produce a Ricci flow via Cheeger–Gromoll exhaustion

Cabezas-Rivas, Esther, and Wilking, Burkhard. "How to produce a Ricci flow via Cheeger–Gromoll exhaustion." Journal of the European Mathematical Society 017.12 (2015): 3153-3194. <http://eudml.org/doc/277682>.

@article{Cabezas2015,
abstract = {We prove short time existence for the Ricci flow on open manifolds of non-negative complex sectional curvature without requiring upper curvature bounds. By considering the doubling of convex sets contained in a Cheeger–Gromoll convex exhaustion and solving the singular initial value problem for the Ricci flow on these closed manifolds, we obtain a sequence of closed solutions of the Ricci flow with non-negative complex sectional curvature which subconverge to a Ricci flow on the open manifold. Furthermore, we find an optimal volume growth condition which guarantees long time existence, and give an analysis of the long time behavior of the Ricci flow. We also construct an explicit example of an immortal non-negatively curved Ricci flow with unbounded curvature for all time.},
author = {Cabezas-Rivas, Esther, Wilking, Burkhard},
journal = {Journal of the European Mathematical Society},
keywords = {Ricci flow; short time existence; Cheeger–Gromoll exhaustion; complex sectional curvature; Ricci flow; short time existence; Cheeger-Gromoll exhaustion; complex sectional curvature},
language = {eng},
number = {12},
pages = {3153-3194},
publisher = {European Mathematical Society Publishing House},
title = {How to produce a Ricci flow via Cheeger–Gromoll exhaustion},
url = {http://eudml.org/doc/277682},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Cabezas-Rivas, Esther
AU - Wilking, Burkhard
TI - How to produce a Ricci flow via Cheeger–Gromoll exhaustion
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 12
SP - 3153
EP - 3194
AB - We prove short time existence for the Ricci flow on open manifolds of non-negative complex sectional curvature without requiring upper curvature bounds. By considering the doubling of convex sets contained in a Cheeger–Gromoll convex exhaustion and solving the singular initial value problem for the Ricci flow on these closed manifolds, we obtain a sequence of closed solutions of the Ricci flow with non-negative complex sectional curvature which subconverge to a Ricci flow on the open manifold. Furthermore, we find an optimal volume growth condition which guarantees long time existence, and give an analysis of the long time behavior of the Ricci flow. We also construct an explicit example of an immortal non-negatively curved Ricci flow with unbounded curvature for all time.
LA - eng
KW - Ricci flow; short time existence; Cheeger–Gromoll exhaustion; complex sectional curvature; Ricci flow; short time existence; Cheeger-Gromoll exhaustion; complex sectional curvature
UR - http://eudml.org/doc/277682
ER -