Accepted Paper

Inserted: 15 mar 2016
Last Updated: 16 may 2017

Journal: Journal of Geometric Analysis
Year: 2016

Abstract:

We use porosity to study differentiability of Lipschitz maps on Carnot groups. Our first result states that directional derivatives of a Lipschitz function act linearly outside a $\sigma$-porous set. The second result states that irregular points of a Lipschitz function form a $\sigma$-porous set. We use these observations to give a new proof of Pansu's theorem for Lipschitz maps from a general Carnot group to a Euclidean space.

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• Porosity@@Differentiability@and@Pansu@s@Theorem@August@15@@Second@Revision@.pdf