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On the converse of Pansu's Theorem
Guido De Philippis, Andrea Marchese, Andrea Merlo +2
We provide a suitable generalisation of Pansu's differentiability theorem to general Radon measures on Carnot groups and we show that if Lipschitz maps between Carnot groups are Pa…
On the density problem in the parabolic space
Andrea Merlo, Mihalis Mourgoglou, Carmelo Puliatti
In this work we extend many classical results concerning the relationship between densities, tangents and rectifiability to the parabolic spaces, namely equipped…
On rectifiable measures in Carnot groups: Marstrand-Mattila rectifiability criterion
Gioacchino Antonelli, Andrea Merlo
In this paper we continue the study of the notion of -rectifiability in Carnot groups. We say that a Radon measure is -rectifiable, for ,…
Unextendable intrinsic Lipschitz curves
Gioacchino Antonelli, Andrea Merlo
In the setting of Carnot groups, we exhibit examples of intrinisc Lipschitz curves of positive -measure that intersect every connected intrinsic Lipschitz curve in a…
On rectifiable measures in Carnot groups: representation
Gioacchino Antonelli, Andrea Merlo
This paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of -rectifiable measure. First, we show t…
Intrinsically Lipschitz functions with normal target in Carnot groups
Gioacchino Antonelli, Andrea Merlo
We provide a Rademacher theorem for intrinsically Lipschitz functions , where is a Borel set, and are complementary…