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

Lai, Yi¹

¹ Department of Mathematics, University of California, Berkeley, Berkeley, CA, United States

Geometry & topology, Tome 25 (2021) no. 7, pp. 3629-3690.

Résumé

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.

Détail

DOI : 10.2140/gt.2021.25.3629

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

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