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


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

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Related projects

Ministry reporting: Yes

Reporting Year: 2019

JUFO rating: 3

Last updated on 2020-17-10 at 23:46