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 ...
Le Donne, Enrico; Lučić, Danka; Pasqualetto, Enrico(Springer, 2022)
We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations ...
We establish regularity of conformal maps between sub-Riemannian manifolds from regularity of Q-harmonic functions, and in particular we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth in all contact ...
We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing ...
The main result of this paper is the following: any weighted Riemannian manifold (M,g,𝜇), i.e., a Riemannian manifold
(M,g) endowed with a generic non-negative Radon measure 𝜇, is infinitesimally Hilbertian, which ...
