Lusin Approximation and Horizontal Curves in Carnot Groups

Gareth Speight

Lusin Approximation and Horizontal Curves in Carnot Groups

Metric Geometry 2015-11-26 v4

Authors: Gareth Speight

Abstract

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.

Keywords

lie groups group theory gamma-convergence and homogenization

Cite

@article{arxiv.1412.2531,
  title  = {Lusin Approximation and Horizontal Curves in Carnot Groups},
  author = {Gareth Speight},
  journal= {arXiv preprint arXiv:1412.2531},
  year   = {2015}
}

Comments

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

Lusin Approximation and Horizontal Curves in Carnot Groups

Abstract

Keywords

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