On the Converse of Pansu’s Theorem

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2024年12月10日

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

摘要

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.