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Producing 3D Ricci flows with nonnegative Ricci curvature via singular Ricci flows

Yi Lai

Geometry & Topology 25 (2021) 3629–3690

We extend the concept of singular Ricci flow by Kleiner and Lott from 3D compact manifolds to 3D complete manifolds with possibly unbounded curvature. As an application of the generalized singular Ricci flow, we show that for any 3D complete Riemannian manifold with nonnegative Ricci curvature, there exists a smooth Ricci flow starting from it. This partially confirms a conjecture by Topping.

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Ricci flow, noncompact, nonnegative Ricci curvature, Ricci flow spacetime, singular Ricci flow, heat kernel, pseudolocality
Mathematical Subject Classification
Primary: 53E20
Received: 14 May 2020
Revised: 11 January 2021
Accepted: 10 February 2021
Published: 25 January 2022
Proposed: Gang Tian
Seconded: Tobias H Colding, Bruce Kleiner
Yi Lai
Department of Mathematics
University of California, Berkeley
Berkeley, CA
United States