On the Converse of Pansu’s Theorem

Guido De Philippis; Andrea Marchese; Andrea Merlo; Andrea Pinamonti; Filip Rindler

doi:10.1007/s00205-024-02059-8

On the Converse of Pansu’s Theorem

Guido De Philippis, Andrea Marchese, Andrea Merlo, Andrea Pinamonti, Filip Rindler

Mathematics

Research output: Contribution to journal › Article › peer-review

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, then μ must be absolutely continuous with respect to the Haar measure of the group.

Original language	English (US)
Article number	3
Journal	Archive for Rational Mechanics and Analysis
Volume	249
Issue number	1
DOIs	https://doi.org/10.1007/s00205-024-02059-8
State	Published - Feb 2025

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-024-02059-8

Cite this

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On the Converse of Pansu’s Theorem

Abstract

ASJC Scopus subject areas

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