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

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.

to appear on Transactions of AMS

References in corpus (1)

• Pseudolocality of Ricci Flow under Integral Bound of Curvature

Cited by in corpus (2)

• Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below
• Smoothing Riemannian Metrics with Bounded Ricci Curvatures in Dimension Four, II