Splitting maps in Type I Ricci flows

Abstract: Harmonic almost splitting maps are an indispensable tool in the study of the singularity structure of non-collapsed Ricci limit spaces. In fact, by recent work of Cheeger-Jiang-Naber the singular stratification is rectifiable, and almost splitting maps are used to construct bi-Lipschitz charts of the singular strata. For this, it is crucial to understand how a splitting map may degenerate at small scales, and when it doesn’t.

In this talk we will discuss similar issues for a parabolic analogue of almost splitting maps, in the context of the Ricci Flow, and present some new results regarding the existence and small scale behavior of almost splitting maps in a Ricci flow with Type I curvature bounds. We will also discuss how these results relate to a conjecture of Perelman on the boundedness of the diameter of a 3d Ricci flow developing a finite time singularity, as we approach the singular time.

link: meet.google.com/wha-yopd-trc

Mathematics

Audience: researchers in the topic

IUT seminar in Geometry, Topology and PDE (IGTP)