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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 ...

• 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 ...

• Space of signatures as inverse limits of Carnot groups 

  Le Donne, Enrico; Züst, Roger (EDP Sciences, 2021)

  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 ...

• Extremal polynomials in stratified groups 

  Le Donne, Enrico; Leonardi, Gian Paolo; Monti, Roberto; Vittone, Davide (International Press, 2018)

  We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal sub-Riemannian extremals ...