Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2

DOI10.1137/19M1271166MaRDI QIDQ5215897

Eero Hakavuori

Publication date: 13 February 2020

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.03214

zbMATH Keywords

geodesicsisometric embeddingssub-Riemannian geometryisometriesCarnot groupssub-Finsler geometry

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Sub-Riemannian geometry (53C17) Optimality conditions for problems involving relations other than differential equations (49K21) Geometric embeddings of metric spaces (30L05)

Related Items (5)

Geodesic fields for Pontryagin type C⁰-Finsler manifolds ⋮ Periodic controls in step 2 strictly convex sub-Finsler problems ⋮ Abnormal trajectories in the sub-Riemannian \((2,3,5,8)\) problem ⋮ Blowups and blowdowns of geodesics in Carnot groups ⋮ Coadjoint orbits and time-optimal problems for step-2 free nilpotent Lie groups

Cites Work

• Unnamed Item
• Isometries of Carnot groups and sub-Finsler homogeneous manifolds
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Existence of tangent lines to Carnot-Carathéodory geodesics
• Isometric embeddings into Heisenberg groups
• Sub-Finsler geodesics on the Cartan group
• Besicovitch covering property on graded groups and applications to measure differentiation
• Control theory from the geometric viewpoint.
• Geodesics and isometries of Carnot groups
• Isometries of nilpotent metric groups
• Strong Sard conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3
• On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures
• Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions
• Non-minimality of corners in subriemannian geometry
• Cut time in sub-riemannian problem on engel group
• On Tangent Cones to Length Minimizers in Carnot--Carathéodory Spaces
• A Comprehensive Introduction to Sub-Riemannian Geometry
• Infinite Geodesics of Sub-Finsler Distances in Heisenberg Groups
• A metric characterization of Carnot groups
• Convex Analysis
• Blowups and blowdowns of geodesics in Carnot groups

This page was built for publication: Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2