Accepted Paper
Inserted: 8 jul 2016
Last Updated: 30 oct 2017
Year: 2016
To appear in ''Measure Theory in Non-Smooth Spaces" (Nicola Gigli, ed), De Gruyter,
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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