Lusin approximation for horizontal curves in step 2 Carnot groups

Enrico Le Donne; Gareth Speight

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arXiv · 1602.02607

Lusin approximation for horizontal curves in step 2 Carnot groups

Enrico Le Donne·Gareth Speight

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Abstract

A Carnot group $\mathbb{G}$ admits Lusin approximation for horizontal curves if for any absolutely continuous horizontal curve $\gamma$ in $\mathbb{G}$ and $\varepsilon>0$, there is a $C^1$ horizontal curve $\Gamma$ such that $\Gamma=\gamma$ and $\Gamma'=\gamma'$ outside a set of measure at most $\varepsilon$. We verify this property for free Carnot groups of step 2 and show that it is preserved by images of Lie group homomorphisms preserving the horizontal layer. Consequently, all step 2 Carnot groups admit Lusin approximation for horizontal curves.

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BibTeX RIS

Enrico Le Donne, Gareth Speight. 2016-02-08. Lusin approximation for horizontal curves in step 2 Carnot groups. https://arxiv.org/abs/1602.02607

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