On the regularity of Ricci flows coming out of metric spaces
speaker: Felix Schulze (University College London)abstract:
We consider smooth, not necessarily complete, Ricci flows, (M,g(t)){t \in (0,T)} with Ric(g(t))\geq−1 and
Rm(g(t))
\leq ct for all t\in(0,T) coming out of metric spaces (M,d0) in the sense that (M,d(g(t)),x0)->(M,d0,x0) as t->0 in the pointed Gromov-Hausdorff sense. In the case that B{g(t)}(x0,1)\Subset M for all t \in (0,T) and d0 is generated by a smooth Riemannian metric in distance coordinates, we show using Ricci-harmonic map heat flow, that there is a corresponding smooth solution \tilde{g}(t){t\in (0,T)} to the \delta-Ricci-DeTurck flow on an Euclidean ball Br(p0)\subset Rn, which can be extended to a smooth solution defined for t\in [0,T). We further show, that this implies that the original solution g can be extended to a smooth solution on B{d0}(x0,r2) for t \in [0,T), in view of the method of Hamilton. This is joint work with Alix Deruelle and Miles Simon.
timetable:
Wed 27 Nov, 16:50 - 17:40, Aula Dini
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