Lusin approximation and horizontal curves in Carnot groups
type: Item
instance of: scholarly article
title: Lusin approximation and horizontal curves in Carnot groups
zbMATH Open document ID: 1406.53039
DOI: 10.4171/RMI/924
author: Gareth Speight
published in: Revista Matemática Iberoamericana
publication date: 2017-03-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1412.2531
review text: Summary: We show that, given an absolutely continuous horizontal curve \(\gamma\) in the Heisenberg group, there is a \(C^{1}\) horizontal curve \(\Gamma\) such that \(\Gamma =\gamma\) and \(\Gamma^\prime =\gamma^\prime\) outside a set of small measure. Conversely, we construct an absolutely continuous horizontal curve in the Engel group with no \(C^{1}\) horizontal approximation.
Mathematics Subject Classification ID: 53C17
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 6694087
zbMATH Keywords: Carnot group
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Engel group
zbMATH Keywords: horizontal curve
zbMATH Keywords: Lusin approximation
zbMATH Keywords: Whitney extension
MaRDI profile type: Publication
arXiv ID: 1412.2531
cites work: Q4441888
OpenAlex ID: W2962848587
description: scientific article