On the Converse of Pansu’s Theorem
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>μ</mml:mi></mml:math> , then <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>μ</mml:mi></mml:math> must be absolutely continuous with respect to the Haar measure of the group.
Authors
- Andrea Marchese (ORCID: https://orcid.org/0000-0002-2066-3501)
- Filip Rindler (ORCID: https://orcid.org/0000-0003-2126-3865)
- Guido De Philippis (ORCID: https://orcid.org/0000-0002-0446-6268)
- Andrea Pinamonti (ORCID: https://orcid.org/0000-0003-1000-8607)
- Andrea Merlo (ORCID: https://orcid.org/0000-0003-4175-619X)
Institutions
- University of the Basque Country (ES)
- University of Trento (IT)
- Courant Institute of Mathematical Sciences (US)
- University of Warwick (GB)
- New York University (US)
Publication Details
- Journal
- Archive for Rational Mechanics and Analysis
- Published
- 2024-12-10
- DOI
- https://doi.org/10.1007/s00205-024-02059-8
- Citations
- 3
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 2.93
Funders
- National Science Foundation
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Università degli Studi di Trento
- HORIZON EUROPE Framework Programme
- European Research Council
- Division of Environmental Biology
- H2020 Marie Skłodowska-Curie Actions