Porosity, Differentiability and Pansu's Theorem

2016/03/15 by Pinamonti, Andrea, Speight, Gareth
#28A75 #43A80 #49Q15 #53C17 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1603.04818

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 σ-porous set. The second result states that irregular points of a Lipschitz function form a σ-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.

Related

• Porosity and Differentiability of Lipschitz Maps from Stratified Groups\n to Banach Homogeneous Groups
• Structure of Porous Sets in Carnot Groups
• Lipschitz spaces over non-porous sets
• On the converse of Pansu's Theorem
• Lipschitz and biLipschitz Maps on Carnot Groups