Universal differentiability sets and maximal directional derivatives in Carnot groups
Functional Analysis
2020-04-10 v3
Abstract
We show that every Carnot group G of step 2 admits a Hausdorff dimension one `universal differentiability set' N such that every real-valued Lipschitz map on G is Pansu differentiable at some point of N. This relies on the fact that existence of a maximal directional derivative of f at a point x implies Pansu differentiability at the same point x. We show that such an implication holds in Carnot groups of step 2 but fails in the Engel group which has step 3.
Cite
@article{arxiv.1705.05871,
title = {Universal differentiability sets and maximal directional derivatives in Carnot groups},
author = {Enrico Le Donne and Andrea Pinamonti and Gareth Speight},
journal= {arXiv preprint arXiv:1705.05871},
year = {2020}
}
Comments
30 pages