Lusin approximation and horizontal curves in Carnot groups
Gareth Speight
University of Cincinnati, USA
![Lusin approximation and horizontal curves in Carnot groups cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-32-issue-4.png&w=3840&q=90)
Abstract
We show that, given an absolutely continuous horizontal curve in the Heisenberg group, there is a horizontal curve such that and outside a set of small measure. Conversely, we construct an absolutely continuous horizontal curve in the Engel group with no horizontal approximation.
Cite this article
Gareth Speight, Lusin approximation and horizontal curves in Carnot groups. Rev. Mat. Iberoam. 32 (2016), no. 4, pp. 1423–1444
DOI 10.4171/RMI/924