A1 Journal article (refereed)
Universal differentiability sets and maximal directional derivatives in Carnot groups (2019)
Le Donne, E., Pinamonti, A., & Speight, G. (2019). Universal differentiability sets and maximal directional derivatives in Carnot groups. Journal de Mathematiques Pures et Appliquees, 121, 83-112. doi:10.1016/j.matpur.2017.11.006
JYU authors or editors
Publication details
All authors or editors: Le Donne, Enrico; Pinamonti, Andrea; Speight, Gareth
Journal or series: Journal de Mathematiques Pures et Appliquees
ISSN: 0021-7824
eISSN: 1776-3371
Publication year: 2019
Volume: 121
Issue number: 0
Pages range: 83-112
Publisher: Elsevier Masson
Publication country: France
Publication language: English
DOI: https://doi.org/10.1016/j.matpur.2017.11.006
Open Access: Publication channel is not openly available
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/60646
Abstract
We show that every Carnot group G of step 2 admits a Hausdorff dimension one ‘universal differentiability set’ N such that every Lipschitz map f : G → R 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.
Keywords: differential geometry; functional analysis
Free keywords: Carnot group; Lipschitz map; Pansu differentiable; directional derivative; universal differentiability set
Contributing organizations
Related projects
- Geometry of subRiemannian groups: regularity of finite-perimeter sets, geodesics, spheres, and isometries with applications and generalizations to biLipschitz homogenous spaces
- Le Donne, Enrico
- Academy of Finland
- GeoMeG Geometry of Metric groups
- Le Donne, Enrico
- European Commission
Ministry reporting: Yes
Reporting Year: 2019
JUFO rating: 3
