On Tangent Cones to Length Minimizers in Carnot--Carathéodory Spaces

DOI10.1137/17M114056XzbMath1397.53047arXiv1707.07990OpenAlexW2964102096MaRDI QIDQ4683910

Davide Vittone, Alessandro Pigati, Roberto Monti

Publication date: 26 September 2018

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

Full work available at URL: https://arxiv.org/abs/1707.07990

zbMATH Keywords

sub-Riemannian geometryCarnot-Carathéodory spacesCarnot groupslength minimizers

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Sub-Riemannian geometry (53C17) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items

The regularity problem for geodesics of the control distance, Strong Sard conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3, Lipschitz Carnot-Carathéodory structures and their limits, Surface measure on, and the local geometry of, sub-Riemannian manifolds, Blowups and blowdowns of geodesics in Carnot groups, On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures, Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2, Fine properties of functions with bounded variation in Carnot-Carathéodory spaces

Cites Work

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• On Carnot-Caratheodory metrics
• End-point equations and regularity of sub-Riemannian geodesics
• Balls and metrics defined by vector fields. I: Basic properties
• Some remarks on the definition of tangent cones in a Carnot-Carathéodory space
• Existence of tangent lines to Carnot-Carathéodory geodesics
• Non-minimality of corners in subriemannian geometry
• Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung
• Nilpotent and High-Order Approximations of Vector Field Systems
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning