Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows

• Published in: Communications on pure and applied mathematics Vol. 73; no. 6; pp. 1141 - 1204
• Main Authors: Brué, Elia, Semola, Daniele
• Format: Journal Article
• Language: English
• Published: New York John Wiley and Sons, Limited 01.06.2020
• Subjects: Fields (mathematics); Green's functions; Regularity

We prove a regularity result for Lagrangian flows of Sobolev vector fields over RCD(K, N) metric measure spaces; regularity is understood with respect to a newly defined quasi‐metric built from the Green function of the Laplacian. Its main application is that RCD(K, N) spaces have constant dimension...