Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

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

Enrico Le Donne — 2017

Analysis and Geometry in Metric Spaces

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 respect to the distance. We present the basic theory of Carnot groups together with several remarks.We consider them as special cases of graded groups and as homogeneous metric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory spaces and...

Ultrarigid tangents of sub-Riemannian nilpotent groups

Enrico Le Donne;  Alessandro Ottazzi;  Ben Warhurst — 2014

Annales de l’institut Fourier

We show that the tangent cone at the identity is not a complete quasiconformal invariant for sub-Riemannian nilpotent groups. Namely, we show that there exists a nilpotent Lie group equipped with left invariant sub-Riemannian metric that is not locally quasiconformally equivalent to its tangent cone at the identity. In particular, such spaces are not locally bi-Lipschitz homeomorphic. The result is based on the study of Carnot groups that are rigid in the sense that their only quasiconformal maps...

Page 1

Download Results (CSV)