Behaviour of the reference measure on $\sf RCD$ spaces under charts

By Nicola Gigli, Enrico Pasqualetto. 2016

89 citations recorded by the source corpus.

Mondino and Naber recently proved that finite dimensional $\sf RCD$ spaces are rectifiable. Here we show that the push-forward of the reference measure under the charts built by them is absolutely continuous with respect to the Lebesgue measure. This result, read in conjunction with another recent work of us, has relevant implications on the structure of tangent spaces to $\sf RCD$ spaces. A key tool that we use is a recent paper by De Philippis-Rindler about the structure of measures on the Euclidean space.

View Paper: https://www.semanticscholar.org/paper/18413e431dfef1fe9004e76561af79497a689f31

Citations in the corpus

• Non-collapsed spaces with Ricci curvature bounded from below (2017, unknown): “Property (2.22) has been proved in [42], [36].”