Geometry and Geometric Analysis Working Group

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Constancy of the dimension for non-smooth spaces with Ricci curvature bounded below via regularity of Lagrangian flows.

Speaker: Elia Bruè

Location: Warren Weaver Hall 1314

Date: Tuesday, March 3, 2020, 11 a.m.

Synopsis:

After a brief introduction to the theory of RCD(K,N) spaces, i.e. metric measure spaces with Ricci curvature bounded below by K and dimension bounded above by N, I will present the constancy of the dimension theorem in this setting. This result generalizes the one obtained by Colding and Naber for Ricci limits. Its proof relies on a new regularity result for flow maps of Sobolev velocity fields. This is based on a joint work with Daniele Semola.