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arXiv · 1704.06385

Ricci Flow recovering from pinched discs

Timothy Carson
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Abstract

We construct smooth solutions to Ricci flow starting from a class of singular metrics and give asymptotics for the forward evolution. The singular metrics heal with a set of points (of codimension at least three) coming out of the singular point. We conjecture that these metrics arise as final-time limits of Ricci flow encountering a Type-I singularity modeled on $\mathbb{R}^{p+1} \times S^q$. This gives a picture of Ricci flow through a singularity, in which a neighborhood of the manifold changes topology from $D^{p+1} \times S^{q}$ to $S^p \times D^{q+1}$ (through the cone over $S^p \times S^q$.) We work in the class of doubly-warped product metrics. We also briefly discuss some possible smooth and non-smooth forward evolutions from other singular initial data.

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Timothy Carson. 2017-04-21. Ricci Flow recovering from pinched discs. https://arxiv.org/abs/1704.06385

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