Radon-Nikodym property and area formula for Banach homogeneous group targets

2012/01/16 by Valentino Magnani, Magnani, Valentino, Tapio Rajala +1
Mathematics · #28A75 #46B22 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #math.FA #math.MG #msc:28A75 #msc:46B22

paper · pdf · doi:10.48550/arxiv.1201.3201

23 pages, 1 figure

arxiv created 2012/01/16 · arxiv updated 2012/01/17

Abstract

We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. We provide a metric area formula that applies to these mappings and more generally to all almost everywhere metrically differentiable Lipschitz mappings defined on a Carnot group.

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