Convex trigonometry with applications to sub-Finsler geometry

DOI10.1070/SM9134zbMath1429.49022arXiv1807.08155OpenAlexW3048391448MaRDI QIDQ5240192

L. V. Lokutsievskiy

Publication date: 24 October 2019

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.08155

zbMATH Keywords

trigonometric functionspolar setconvex analysissub-Finsler geometryphysical pendulum equation

Mathematics Subject Classification ID

Convex sets in (2) dimensions (including convex curves) (52A10) Functions of one variable (26A99) Euclidean analytic geometry (51N20) Sub-Riemannian geometry (53C17) Optimality conditions for free problems in two or more independent variables (49K10)

Related Items (12)

Geodesic fields for Pontryagin type C⁰-Finsler manifolds ⋮ Control of a mobile robot with a trailer based on nilpotent approximation ⋮ Antinorms on cones: duality and applications ⋮ Extremal trajectories in a time-optimal problem on the group of motions of a plane with admissible control in a circular sector ⋮ An isoperimetric problem on the Lobachevsky plane with a left-invariant Finsler structure ⋮ Local \(L^1\) sub-Finsler geometry in dimension 3: non-generic cases ⋮ Extremals of a left-invariant sub-Finsler metric on the Engel group ⋮ Explicit formulae for geodesics in left-invariant sub-Finsler problems on Heisenberg groups via convex trigonometry ⋮ Explicit solutions for a series of optimization problems with 2-dimensional control via convex trigonometry ⋮ Neighborhood of the second-order singular regime in problems with control in a disk ⋮ Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry ⋮ The isoperimetric problem for regular and crystalline norms in \({\mathbb{H}}^1\)

Cites Work

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• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Homogeneous manifolds with intrinsic metric. I
• Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions
• Extremal trajectories in a nilpotent sub-Riemannian problem on the Engel group
• Exponential map in the generalized Dido problem
• The Isoperimetric Problem in the Minkowski Plane

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