论潘素定理的逆

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2024-12-10 DOI:10.1007/s00205-024-02059-8

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

引用次数: 0

摘要

我们将Pansu的可微性定理推广到卡诺群上的一般Radon测度，并证明了如果卡诺群之间的Lipschitz映射对于某些Radon测度\(\mu \)几乎处处都是潘可微的，那么\(\mu \)对于群的Haar测度一定是绝对连续的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.