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.File in questo prodotto:
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