Lusin approximation for horizontal curves in step 2 Carnot groups

A Carnot group G admits Lusin approximation for horizontal curves if for any absolutely continuous horizontal curve γ in G and ε > 0 , there is a C 1 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...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 55; no. 5; pp. 1 - 22
Main Authors Le Donne, Enrico, Speight, Gareth
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2016
Springer Nature B.V
Subjects
Analysis
Approximation
Calculus of Variations and Optimal Control; Optimization
Control
Homomorphisms
Lie groups
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
Traffic accidents & safety
28C15
43A80
49Q15
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Summary:A Carnot group G admits Lusin approximation for horizontal curves if for any absolutely continuous horizontal curve γ in G and ε > 0 , there is a C 1 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.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-016-1054-z