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• A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries 

  Le Donne, Enrico (De Gruyter Open, 2017)

  Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with ...

• Rigidity, counting and equidistribution of quaternionic Cartan chains 

  Parkkonen, Jouni; Paulin, Frédéric (Universite Clermont Auvergne, 2022)

  In this paper, we prove an analog of Cartan’s theorem, saying that the chain-preserving transformations of the boundary of the quaternionic hyperbolic spaces are projective transformations. We give a counting and ...

• Lipschitz Carnot-Carathéodory Structures and their Limits 

  Antonelli, Gioacchino; Le Donne, Enrico; Nicolussi Golo, Sebastiano (Springer Science and Business Media LLC, 2023)

  In this paper we discuss the convergence of distances associated to converging structures of Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove that, under a mild controllability assumption ...

• Conformality and Q-harmonicity in sub-Riemannian manifolds 

  Capogna, Luca; Citti, Giovanna; Le Donne, Enrico; Ottazzi, Alessandro (Elsevier Masson, 2019)

  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 ...

• Semigenerated Carnot algebras and applications to sub-Riemannian perimeter 

  Le Donne, Enrico; Moisala, Terhi (Springer, 2021)

  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 ...