Geodesic
How to produce a Ricci flow via Cheeger–Gromoll exhaustion
Journal of the European Mathematical Society, Tome 17 (2015) no. 12, pp. 3153-3194 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/582
Classification : 53-XX, 35-XX, 58-XX
Keywords: Ricci flow, short time existence, Cheeger–Gromoll exhaustion, complex sectional curvature 
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     author = {Esther Cabezas-Rivas and Burkhard Wilking},
     title = {How to produce a {Ricci} flow via {Cheeger{\textendash}Gromoll} exhaustion},
     journal = {Journal of the European Mathematical Society},
     pages = {3153--3194},
     year = {2015},
     volume = {17},
     number = {12},
     doi = {10.4171/jems/582},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/582/}
}
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Esther Cabezas-Rivas; Burkhard Wilking. How to produce a Ricci flow via Cheeger–Gromoll exhaustion. Journal of the European Mathematical Society, Tome 17 (2015) no. 12, pp. 3153-3194. doi: 10.4171/jems/582

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