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

created by pasqualetto on 18 Jul 2016
modified on 30 Nov 2016

[BibTeX]

Preprint

Inserted: 18 jul 2016
Last Updated: 30 nov 2016

Pages: 17
Year: 2016

Abstract:

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.