Topics in the geometry of non-Riemannian lie groups
PublisherUniversity of Jyväskylä
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- Väitöskirjat 
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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 ...
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 ...
Antonelli, Gioacchino; Le Donne, Enrico; Nicolussi Golo, Sebastiano (Springer Science and Business Media LLC, 2022)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 ...
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 ...
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 ...