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

By Elia Brué, Daniele Semola. Communications on Pure and Applied Mathematics, 2018

149 citations recorded by the source corpus.

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. In this way we generalize to such an abstract framework a result proved by Colding‐Naber for Ricci limit spaces, introducing ingredients that are new even in the smooth setting. © 2019 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/eb6db1bb9506f1b6519eeac12ebd3bafc77571b9

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In Applied Mathematics

1. Enrico Pasqualetto
2. Elia Brué
3. Semola Daniele

In Geometry and Topology

1. Semola Daniele
2. Elia Brué
3. Enrico Pasqualetto

Citations in the corpus

• Rectifiability of the reduced boundary for sets of finite perimeter over $\RCD(K,N)$ spaces. (2019, background): “12 ELIA BRUÈ, ENRICO PASQUALETTO, AND DANIELE SEMOLA After the works [31, 42, 32, 21, 38] and [12] we have the following structure theorem for RCD(K,N) spaces.”