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arXiv · 1510.04332

Pseudo-locality for a coupled Ricci flow

Bin Guo·Zhijie Huang·Duong H. Phong
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Abstract

Let $(M,g,ϕ)$ be a solution to the Ricci flow coupled with the heat equation for a scalar field $ϕ$. We show that a complete, $κ$-noncollapsed solution $(M,g,ϕ)$ to this coupled Ricci flow with a Type I singularity at time $T<\infty$ will converge to a non-trivial Ricci soliton after parabolic rescaling, if the base point is Type I singular. A key ingredient is a version of Perelman pseudo-locality for the coupled Ricci flow.

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Bin Guo, Zhijie Huang, Duong H. Phong. 2015-11-25. Pseudo-locality for a coupled Ricci flow. https://arxiv.org/abs/1510.04332

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