AI Article Synopsis
- The authors extend Pansu's differentiability theorem to apply to general Radon measures on Carnot groups.
- They demonstrate that Lipschitz maps between Carnot groups that are almost everywhere Pansu-differentiable for specific Radon measures must be absolutely continuous.
- This absolute continuity is defined in relation to the Haar measure of the group, which is a key measure used in the study of groups.
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 , then must be absolutely continuous with respect to the Haar measure of the group.
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Source |
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11655620 | PMC |
| http://dx.doi.org/10.1007/s00205-024-02059-8 | DOI Listing |
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