On a conjecture of Cheeger

2016/07/08 by De Philippis, Guido, Marchese, Andrea, Rindler, Filip · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1607.02554

Abstract

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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