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

TL;DR

This paper establishes a Rademacher-type theorem and a metric area formula for Lipschitz mappings from Carnot groups to Banach homogeneous groups, extending differentiability and measure-theoretic results in geometric analysis.

Contribution

It introduces a Radon-Nikodym property for Banach homogeneous groups and proves a metric area formula applicable to Lipschitz mappings on Carnot groups.

Findings

Proved a Rademacher-type theorem for Lipschitz maps into Banach homogeneous groups.

Established a metric area formula for almost everywhere metrically differentiable Lipschitz maps.

Extended measure-theoretic tools to a broader class of geometric structures.

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.