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 C1horizontal 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.
Lusin approximation for horizontal curves in step 2 Carnot groups
Le Donne, Enrico;
2016-01-01
Abstract
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 C1horizontal 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.File in questo prodotto:
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