Long-time analysis of 3 dimensional Ricci flow I

Details Long-time analysis of 3 dimensional Ricci flow I Long-time analysis of 3 dimensional Ricci flow I

2011-12-21

arxiv.org/abs/1112.5125v1

Mathematics

Differential Geometry

25 pages

Scientific paper

In this paper we analyze the long-time behaviour of 3 dimensional Ricci flow with surgery. We prove that under the topological condition that the initial manifold only has non-aspherical or hyperbolic components in its geometric decomposition, there are only finitely many surgeries and the curvature is bounded by $C t^{-1}$ for large $t$. This answers an open question in Perelman's work, which was made more precise by Lott and Tian, for this class of initial topologies. More general classes will be discussed in subsequent papers using similar methods.

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