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On the long-time behavior of type-III Ricci flow solutions

John Lott
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Abstract

We show that three-dimensional homogeneous Ricci flow solutions that admit finite-volume quotients have long-time limits given by expanding solitons. We show that the same is true for a large class of four-dimensional homogeneous solutions. We give an extension of Hamilton's compactness theorem that does not assume a lower injectivity radius bound, in terms of Riemannian groupoids. Using this, we show that the long-time behavior of type-III Ricci flow solutions is governed by the dynamics of an R^+ action on a compact space.

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John Lott. 2007-05-29. On the long-time behavior of type-III Ricci flow solutions. https://arxiv.org/abs/math/0509639

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