Calculus of Variations and Geometric Measure Theory

G. Speight

Lusin Approximation and Horizontal Curves in Carnot Groups

created by speight on 08 Dec 2014
modified on 16 May 2017


Published Paper

Inserted: 8 dec 2014
Last Updated: 16 may 2017

Journal: Revista Matematica Iberoamericana
Volume: 32
Number: 4
Pages: 1425-1446
Year: 2015

ArXiv: 1412.2531 PDF

21 pages. Corrected a technical error in the argument for the Heisenberg group and added previously omitted proofs. Improved the exposition and corrected typos as suggested by referees. To appear in Revista Matematica Iberoamericana


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 $\Gamma'=\gamma'$ outside a set of small measure. Conversely, we construct an absolutely continuous horizontal curve in the Engel group with no $C^1$ horizontal approximation.

Tags: GeMeThNES