Short-time existence of the Ricci flow on noncompact Riemannian manifolds

Guoyi Xu

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arXiv · 0907.5604

Short-time existence of the Ricci flow on noncompact Riemannian manifolds

Guoyi Xu

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Abstract

In this paper, we give the first detailed proof of the short-time existence of Deane Yang's local Ricci flow. Then using the local Ricci flow, we prove short-time existence of the Ricci flow on noncompact manifolds, whose Ricci curvature has global lower bound and sectional curvature has only local average integral bound. The short-time existence of the Ricci flow on noncompact manifolds with bounded curvature was studied by Wan-Xiong Shi in 1990s. As a corollary of our main theorem, we get the short-time existence part of Shi's theorem in this more general context.

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Guoyi Xu. 2009-07-31. Short-time existence of the Ricci flow on noncompact Riemannian manifolds. https://arxiv.org/abs/0907.5604

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