Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian Flows

Daniele Semola
Thursday, April 5, 2018 - 14:00

The class of RCD(K,N) metric measure spaces was introduced by Gigli adding to the curvature-dimension CD(K,N) condition the request of linearity of the heat flow.
The aim of this seminar is twofold. In the first part we present some regularity results for Lagrangian Flows of Sobolev vector fields over finite dimensional RCD spaces. The regularity is measured in terms of a newly defined quasi-distance built from the Green function of the Laplacian.
In the second part of the talk we apply these results to prove that on any RCD(K,N) space the dimension of the tangent space is the same almost everywhere.
This is based on a work in progress with Elia Brue’.

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