59 citations · 162 across the 30 of their papers we have counts for
7 papers · 1 filter
Asymptotics of Riemannian Lie groups with nilpotency step 2
Enrico Le Donne, Luca Nalon, Sebastiano Nicolussi Golo +1
We derive sharp estimates comparing asymptotic Riemannian or sub-Riemannian metrics in 2-step nilpotent Lie groups. For each metric, we construct a Carnot metric whose square remai…
Metric Lie Groups. Carnot-Carathéodory spaces from the homogeneous viewpoint
Enrico Le Donne
This book explores geometries defined by left-invariant distance functions on Lie groups, with a particular focus on nilpotent groups and Carnot groups equipped with geodesic dista…
Escape from compact sets of normal curves in Carnot groups
Enrico Le Donne, Nicola Paddeu
In the setting of subFinsler Carnot groups, we consider curves that satisfy the normal equation coming from the Pontryagin Maximum Principle. We show that, unless it is constant, e…
A sub-Finsler problem on the Cartan group
A. Ardentov, E. Le Donne, Yu. Sachkov
In this paper we study a sub-Finsler geometric problem on the free-nilpotent group of rank 2 and step 3. Such a group is also called Cartan group and has a natural structure of Car…
Non-minimality of corners in subriemannian geometry
Eero Hakavuori, Enrico Le Donne
We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result…
Extremal polynomials in stratified groups
Enrico Le Donne, Gian Paolo Leonardi, Roberto Monti +1
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 characterizat…