From the 1 of 8 linked papers with an AI index.
5 papers · 1 filter
Sard property for rank 2 polarizations in metabelian Lie groups
Enrico Le Donne, Antonio Lerario, Luca Nalon +2
The paper establishes dimension bounds for abnormal and Goh‑abnormal sets in rank‑2 polarized metabelian Lie groups, proving that the endpoint map satisfies the Sard property and t…
Quantitative versions of Pansu Asymptotic Theorem and of Mitchell Tangent Theorem
Enrico Le Donne, Sebastiano Nicolussi Golo, Andrea Tettamanti
We quantitatively study the speed of convergence of geodesic Lie groups to their metric limits. For nilpotent geodesic Lie groups, we give estimates on the difference of the origin…
Normal Curves in Sub-Finsler Lie Groups: Branching for Strongly Convex Norms and Face Stability for Polyhedral Norms
Enrico Le Donne, Sebastiano Nicolussi Golo, Nicola Paddeu
We consider Lie groups equipped with left-invariant subbundles of their tangent bundles and norms on them. On these sub-Finsler structures, we study the normal curves in the sense…
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…