On the converse of Pansu's Theorem

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

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arXiv · 2211.06081

On the converse of Pansu's Theorem

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

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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.

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Guido De Philippis, Andrea Marchese, Andrea Merlo, Andrea Pinamonti, Filip Rindler. 2022-11-11. On the converse of Pansu's Theorem. https://arxiv.org/abs/2211.06081

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