Extreme properties of curves with bounded curvature on a sphere

DOI10.1007/s10883-014-9221-zzbMath1321.53064arXiv1605.09157OpenAlexW1978353062MaRDI QIDQ2352265

Kostiantyn Drach, Alexander A. Borisenko

Publication date: 30 June 2015

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.09157

zbMATH Keywords

isoperimetric inequality\(\lambda\)-convex curvePontryagin's Maximal Principle

Mathematics Subject Classification ID

Global submanifolds (53C40) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (4)

Reverse isoperimetric inequality in two-dimensional Alexandrov spaces ⋮ Inradius estimates for convex domains in 2-dimensional Alexandrov spaces ⋮ The estimation of the length of a convex curve in two-dimensional Alexandrov space ⋮ A sausage body is a unique solution for a reverse isoperimetric problem

Cites Work

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• Zur Begründung der elementaren Inhaltslehre in der hyperbolischen Ebene
• An Application of the Maximum Principle to the Geometry of Plane Curves
• Closeness to spheres of hypersurfaces with normal curvature bounded below

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