Intrinsically Lipschitz functions with normal target in Carnot groups

Författare

  • Gioacchino Antonelli Scuola Normale Superiore
  • Andrea Merlo Universitá di Pisa

Nyckelord:

Carnot groups, intrinsically Lipschitz functions, Rademacher theorem, area formula

Abstract

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.
Sektion
Articles

Publicerad

2021-06-22

Referera så här

Antonelli, G., & Merlo, A. (2021). Intrinsically Lipschitz functions with normal target in Carnot groups. Annales Fennici Mathematici, 46(1), 571–579. Hämtad från https://afm.journal.fi/article/view/109691