We provide a Rademacher theorem for intrinsically Lipschitz functions $\phi\colon U\subseteq\mathbf{W}\to\mathbf{L}$, where $U$ is a Borel set, $\mathbf{W}$ and $\mathbf{L}$ are complementary subgroups of a Carnot group, where we require that $\mathbf{L}$ is a normal subgroup. Our hypotheses are satisfied for example when $\mathbf{W}$ is a horizontal subgroup. Moreover, we provide an area formula for this class of intrinsically Lipschitz functions.
@article{AFM_2021_46_1_a33,
author = {Gioacchino Antonelli and Andrea Merlo},
title = {Intrinsically {Lipschitz} functions with normal target in {Carnot} groups},
journal = {Annales Fennici Mathematici},
pages = {571--579},
year = {2021},
volume = {46},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a33/}
}
TY - JOUR
AU - Gioacchino Antonelli
AU - Andrea Merlo
TI - Intrinsically Lipschitz functions with normal target in Carnot groups
JO - Annales Fennici Mathematici
PY - 2021
SP - 571
EP - 579
VL - 46
IS - 1
UR - http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a33/
LA - en
ID - AFM_2021_46_1_a33
ER -
%0 Journal Article
%A Gioacchino Antonelli
%A Andrea Merlo
%T Intrinsically Lipschitz functions with normal target in Carnot groups
%J Annales Fennici Mathematici
%D 2021
%P 571-579
%V 46
%N 1
%U http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a33/
%G en
%F AFM_2021_46_1_a33
Gioacchino Antonelli; Andrea Merlo. Intrinsically Lipschitz functions with normal target in Carnot groups. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 571-579. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a33/
