Universal differentiability sets and maximal directional derivatives in Carnot groups
Year of publication
2019
Authors
Le Donne, Enrico; Pinamonti, Andrea; Speight, Gareth
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.
Show moreOrganizations and authors
University of Jyväskylä
Le Donne Enrico 
Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Publisher
Volume
121
Pages
83-112
ISSN
Publication forum
Publication forum level
3
Open access
Open access in the publisher’s service
No
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object]
Publication country
France
Internationality of the publisher
International
Language
English
International co-publication
Yes
Co-publication with a company
No
DOI
10.1016/j.matpur.2017.11.006
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes