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On a conjecture of Cheeger

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arxiv 1607.02554 v2 pith:S7ZP4DHJ submitted 2016-07-08 math.MG

classification math.MG
keywords cheegerconjecturedifferentiabilitylipschitzmeasurestructureabsolutelyallows
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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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