Work

On the Converse of Pansu’s Theorem

Year: 2024

Type: article

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

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-024-02059-8

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

Institutions: Courant Institute of Mathematical Sciences, New York University, University of Trento, University of the Basque Country, University of Warwick

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890