Lusin approximation for horizontal curves in step 2 Carnot groups

2016/02/08 by Enrico Le Donne, Donne, Enrico Le, Gareth Speight +1 · 1 citation
Mathematics · #28C15 #43A80 #49Q15 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #math.DG #math.FA #math.MG #msc:28C15 #msc:43A80 #msc:49Q15

paper · pdf · doi:10.48550/arxiv.1602.02607

25 pages

arxiv created 2016/02/08 · openalex publication_date 2016/02/08 · arxiv updated 2016/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Carnot group \mathbbG admits Lusin approximation for horizontal curves if for any absolutely continuous horizontal curve γ in \mathbbG and ε>0, there is a C¹ horizontal curve Γ such that Γ=γ and Γ'=γ' outside a set of measure at most ε. 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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