Related papers: Intrinsically Lipschitz graphs on semidirect produ…

We introduce a notion of intrinsically Lipschitz graphs in the context of metric spaces. This is a broad generalization of what in Carnot groups has been considered by Franchi, Serapioni, and Serra Cassano, and later by many others. We…

We focus our attention on the notion of intrinsic Lipschitz graphs, inside a special class of metric spaces i.e. the Carnot groups. More precisely, we provide a characterization of locally intrinsic Lipschitz functions in Carnot groups of…

Le Donne and the author introduced the so-called intrinsically Lipschitz sections of a fixed quotient map $\pi$ in the context of metric spaces. Moreover, the author introduced the concept of intrinsic Cheeger energy when the quotient map…

The main result of the present paper is a Rademacher-type theorem for intrinsic Lipschitz graphs of codimension $k\leq n$ in sub-Riemannian Heisenberg groups $\mathbb H^n$. For the purpose of proving such a result we settle several related…

We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneous subgroup. This provides counterexamples to a Rademacher…

In the setting of Carnot groups, we are concerned with the rectifiability problem for subsets that have finite sub-Riemannian perimeter. We introduce a new notion of rectifiability that is, possibly, weaker than the one introduced by…

In the setting of Carnot groups, we exhibit examples of intrinisc Lipschitz curves of positive $\mathcal{H}^1$-measure that intersect every connected intrinsic Lipschitz curve in a $\mathcal{H}^1$-negligible set. As a consequence such…

We introduce a definition of intrinsically quasi-symmetric sections in metric spaces and we prove the Ahlfors-David regularity for this class of sections. We follow a recent result by Le Donne and the author where we generalize the notion…

We focus our attention on the notion of intrinsic Lipschitz graphs, inside a subclass of Carnot groups of step 2 which includes a corank 1 Carnot groups (and so the Heisenberg groups), Free groups of step 2 and the complexified Heisenberg…

Recently, Le Donne and the author introduce a notion of intrinsically Lipschitz graphs in metric spaces. The idea of this paper is to investigate about the properties of the intrinsically Lipschitz constants. More precisely, we give the…

We prove that the boundary of an almost minimizer of the intrinsic perimeter in a plentiful group can be approximated by intrinsic Lipschitz graphs. Plentiful groups are Carnot groups of step~$2$ whose center of the Lie algebra is generated…

This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group $\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every intrinsic $L$-Lipschitz…

The aim of this article is to prove a Lipschitz extension theorem for partially defined Lipschitz maps to jet spaces endowed with a left-invariant sub-Riemannian Carnot-Carath\'eodory distance. The jet spaces give a model for a certain…

This paper contributes to the generalization of Rademacher's differentiability result for Lipschitz functions when the domain is infinite dimensional and has nonabelian group structure. We introduce the notion of metric scalable groups…

We provide a Rademacher theorem for intrinsically Lipschitz functions $\phi:U\subseteq \mathbb W\to \mathbb L$, where $U$ is a Borel set, $\mathbb W$ and $\mathbb L$ are complementary subgroups of a Carnot group, where we require that…

A special type of coarea inequality is proved for compositions of intrinsically Lipschitz mappings of Carnot groups with projections along horizontal vector fields. It is proved that the equality is achieved for mappings with finite…

We prove non-extendability results for Lipschitz maps with target space being jet spaces equipped with a left-invariant Riemannian distance, as well as jet spaces equipped with a left-invariant sub-Riemannian Carnot-Caratheodory distance.…

This paper contributes to the study of sets of finite intrinsic perimeter in Carnot groups. Our intent is to characterize in which groups the only sets with constant intrinsic normal are the vertical half-spaces. Our viewpoint is algebraic:…

This paper deals with the problem of finding bi-Lipschitz behavior in non-degenerate Lipschitz maps between metric measure spaces. Specifically, we study maps from (subsets of) Ahlfors regular PI spaces into sub-Riemannian Carnot groups. We…

We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are…