Geodesic
Intrinsically Lipschitz functions with normal target in Carnot groups
Gioacchino Antonelli1 ; Andrea Merlo2
1 Scuola Normale Superiore
2 Universitá di Pisa
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 571-579.

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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.
Keywords: Carnot groups, intrinsically Lipschitz functions, Rademacher theorem, area formula

Gioacchino Antonelli 1 ; Andrea Merlo 2

1 Scuola Normale Superiore
2 Universitá di Pisa 
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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/