English

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 μ\mu, then μ\mu 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}
}