- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:11
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
17
2015
12
How to produce a Ricci flow via Cheeger–Gromoll exhaustion
Esther
Cabezas-Rivas
J. W. Goethe-Universität, FRANKFURT A.M., GERMANY
Burkhard
Wilking
Universität Münster, MÜNSTER, GERMANY
Ricci flow, short time existence, Cheeger–Gromoll exhaustion, complex sectional curvature
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.
Differential geometry
Partial differential equations
Global analysis, analysis on manifolds
3153
3194
10.4171/JEMS/582
http://www.ems-ph.org/doi/10.4171/JEMS/582