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

Lai, Yi

doi:10.2140/gt.2021.25.3629

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

Yi Lai

Geometry & Topology 25 (2021) 3629–3690

DOI: 10.2140/gt.2021.25.3629

Abstract

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.

Keywords

Ricci flow, noncompact, nonnegative Ricci curvature, Ricci flow spacetime, singular Ricci flow, heat kernel, pseudolocality

Mathematical Subject Classification

Primary: 53E20

References

Publication

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

Authors

Yi Lai
Department of Mathematics University of California, Berkeley Berkeley, CA United States

Volume 25, issue 7 (2021)