On the regularity of Ricci flows coming out of metric spaces.

Abstract: Joint work with Alix Deruelle, Felix Schulze

We consider solutions to Ricci flow defined on manifolds M for a time interval $(0,T)$ whose Ricci curvature is bounded uniformly in time from below, and for which the norm of the full curvature tensor at time $t$ is bounded by $c/t$ for some fixed constant $c>1$ for all $t \in (0,T)$. From previous works, it is known that if the solution is complete for all times $t>0$, then there is a limit metric space $(M,d_0)$, as time t approaches zero. We show : if there is a open region $V$ on which $(V,d_0)$ is *smooth*, then the solution can be extended smoothly to time zero on $V$.

Mathematics

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

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