Showing items with similar title or keywords.

• 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 ...

• 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 ...

• Assouad Dimension, Nagata Dimension, and Uniformly Close Metric Tangents 

  Le Donne, Enrico; Rajala, Tapio (Indiana University, 2015)

  We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper ...

• Topics in the geometry of non-Riemannian lie groups 

  Nicolussi Golo, Sebastiano (University of Jyväskylä, 2017)

• Universal Infinitesimal Hilbertianity of Sub-Riemannian Manifolds 

  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 ...