4 papers · 1 filter
Sard property for rank 2 polarizations in metabelian Lie groups
Enrico Le Donne, Antonio Lerario, Luca Nalon +2
We provide sharp bounds on the dimension of the abnormal set for rank polarizations on metabelian Lie groups, establishing the Sard property for the end-point map of such group…
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…
On the H-type deviation of step two Carnot groups
Luca Nalon, Jeremy T. Tyson
The H-type deviation, , of a step two Carnot group quantifies the extent to which deviates from the geometrically and algebraically trac…
The Sard problem in step 2 and in filiform Carnot groups
Francesco Boarotto, Luca Nalon, Davide Vittone
We study the Sard problem for the endpoint map in some well-known classes of Carnot groups. Our first main result deals with step 2 Carnot groups, where we provide lower bounds (de…