Calculus of Variations and Geometric Measure Theory
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G. De Philippis - A. Marchese - F. Rindler

On a conjecture of Cheeger

created by dephilipp on 08 Jul 2016
modified on 10 Oct 2016


Accepted Paper

Inserted: 8 jul 2016
Last Updated: 10 oct 2016

Year: 2016

To appear in ''Measure Theory in Non-Smooth Spaces" (Nicola Gigli, ed), De Gruyter,


This note details how a recent structure theorem for normal $1$-currents proved by the first and third author allows to prove a conjecture of Cheeger concerning the structure of Lipschitz differentiability spaces. More precisely, we show that the push-forward of the measure from a Lipschitz differentiability space under a chart is absolutely continuous with respect to Lebesgue measure.


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