Calculus of Variations and Geometric Measure Theory

G. De Philippis - A. Marchese - A. Merlo - A. Pinamonti - F. Rindler

On the converse of Pansu's Theorem

created by marchese on 09 Nov 2022
modified by dephilipp on 05 Jun 2023


Submitted Paper

Inserted: 9 nov 2022
Last Updated: 5 jun 2023

Year: 2022

ArXiv: 2211.06081 PDF


We provide a suitable generalisation of Pansu's differentiability theorem to general Radon measures on Carnot groups and we show that if Lipschitz maps between Carnot groups are Pansu-differentiable almost everywhere for some Radon measures $\mu$, then $\mu$ must be absolutely continuous with respect to the Haar measure of the group.