# Porosity, Differentiability and Pansu's Theorem

created by pinamonti on 15 Mar 2016
modified by speight on 16 May 2017

[BibTeX]

Accepted Paper

Inserted: 15 mar 2016
Last Updated: 16 may 2017

Journal: Journal of Geometric Analysis
Year: 2016

ArXiv: 1603.04818 PDF

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.