Calculus of Variations and Geometric Measure Theory

G. Antonelli - A. Merlo

Intrinsically Lipschitz functions with normal targets in Carnot groups

created by antonelli on 05 Jun 2020
modified on 31 Mar 2021


Accepted Paper

Inserted: 5 jun 2020
Last Updated: 31 mar 2021

Journal: Ann. Acad. Sci. Fenn. Math.
Year: 2020

ArXiv: 2006.02782 PDF


We provide a Rademacher theorem for intrinsically Lipschitz functions $\phi:U\subseteq \mathbb W\to \mathbb L$, where $U$ is a Borel set, $\mathbb W$ and $\mathbb L$ are complementary subgroups of a Carnot group, where we require that $\mathbb W$ is a Carnot subgroup and $\mathbb L$ 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.

Tags: GeoMeG