This is an announcement for the paper “Porosity and Differentiability of Lipschitz Maps from Stratified Groups to Banach Homogeneous Groups” by Valentino Magnanihttps://arxiv.org/find/math/1/au:+Magnani_V/0/1/0/all/0/1, Andrea Pinamontihttps://arxiv.org/find/math/1/au:+Pinamonti_A/0/1/0/all/0/1, Gareth Speighthttps://arxiv.org/find/math/1/au:+Speight_G/0/1/0/all/0/1.
Abstract: Let $f$ be a Lipschitz map from a subset $A$ of a stratified group to a Banach homogeneous group. We show that directional derivatives of $f$ act as homogeneous homomorphisms at density points of $A$ outside a $sigma$-porous set. At density points of $A$ we establish a pointwise characterization of differentiability in terms of directional derivatives. We use these new results to obtain an alternate proof of almost everywhere differentiability of Lipschitz maps from subsets of stratified groups to Banach homogeneous groups satisfying a suitably weakened Radon-Nikodym property. As a consequence we also get an alternative proof of Pansu's Theorem.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1706.01782