On the converse of Pansu's Theorem
Metric Geometry
2022-11-14 v1 Analysis of PDEs
Classical Analysis and ODEs
Abstract
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 , then must be absolutely continuous with respect to the Haar measure of the group.
Keywords
Cite
@article{arxiv.2211.06081,
title = {On the converse of Pansu's Theorem},
author = {Guido De Philippis and Andrea Marchese and Andrea Merlo and Andrea Pinamonti and Filip Rindler},
journal= {arXiv preprint arXiv:2211.06081},
year = {2022}
}