We provide a Rademacher theorem for intrinsically Lipschitz functions φ: U ⊆ W → L, where U is a Borel set, W and L are complementary subgroups of a Carnot group, where we require that L is a normal subgroup. Our hypotheses are satisfied for example when W is a horizontal subgroup. Moreover, we provide an area formula for this class of intrinsically Lipschitz functions.

Intrinsically Lipschitz functions with normal target in Carnot groups

Antonelli, Gioacchino;Merlo, Andrea
2021

Abstract

We provide a Rademacher theorem for intrinsically Lipschitz functions φ: U ⊆ W → L, where U is a Borel set, W and L are complementary subgroups of a Carnot group, where we require that L is a normal subgroup. Our hypotheses are satisfied for example when W is a horizontal subgroup. Moreover, we provide an area formula for this class of intrinsically Lipschitz functions.
2021
Settore MATH-03/A - Analisi matematica
Area formula; Carnot groups; Intrinsically lipschitz functions; Rademacher theorem;
   Geometry of Metric groups
   GeoMeG
   European Commission
   Horizon 2020 Framework Programme
   713998
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/146784
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