17 citations · 51 across the 15 of their papers we have counts for
11 papers · 1 filter
Carnot rectifiability and Alberti representations
Gioacchino Antonelli, Enrico Le Donne, Andrea Merlo
A metric measure space is said to be Carnot-rectifiable if it can be covered up to a null set by countably many biLipschitz images of compact sets of a fixed Carnot group. In this…
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 sets with unit Hausdorff density in homogeneous groups
Antoine Julia, Andrea Merlo
It is a longstanding conjecture that given a subset of a metric space, if has finite Hausdorff measure in dimension and has unit density…
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…
On rectifiable measures in Carnot groups: existence of density
Gioacchino Antonelli, Andrea Merlo
In this paper we start a detailed study of a new notion of rectifiability in Carnot groups: we say that a Radon measure is -rectifiable, for , if it h…
Marstrand-Mattila rectifiability criterion for -codimensional measures in Carnot Groups
Andrea Merlo
This paper is devoted to show that the flatness of tangents of -codimensional measures in Carnot Groups implies -rectifiability. As applications we prove that me…
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…
Geometry of -codimensional measures in Heisenberg groups
Andrea Merlo
This paper is devoted to the study of tangential properties of measures with density in the Heisenberg groups . Among other results we prove that measures with $(2n+1…