Intrinsically Lipschitz functions with normal target in Carnot groups

2020/06/04 by Antonelli, Gioacchino, Merlo, Andrea · 1 citation
#22E25 #26A16 #28A75 #49Q15 #53C17 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2006.02782

Abstract

We provide a Rademacher theorem for intrinsically Lipschitz functions ϕ:U⊆ \mathbb W→ \mathbb L, where U is a Borel set, \mathbb W and \mathbb L are complementary subgroups of a Carnot group, where we require that \mathbb L is a normal subgroup. Our hypotheses are satisfied for example when \mathbb W is a horizontal subgroup. Moreover, we provide an area formula for this class of intrinsically Lipschitz functions.

Cited by

• On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 2

Related

• Intrinsic Lipschitz graphs in Carnot groups of step 2
• Intrinsically Lipschitz graphs on semidirect products of groups
• Unextendable intrinsic Lipschitz curves
• Nowhere differentiable intrinsic Lipschitz graphs
• Radon-Nikodym property and area formula for Banach homogeneous group targets