Extreme properties of curves with bounded curvature on a sphere
Differential Geometry
2016-05-31 v1 Optimization and Control
Abstract
We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for convex curves whose curvatures are bounded from above.
Keywords
Cite
@article{arxiv.1605.09157,
title = {Extreme properties of curves with bounded curvature on a sphere},
author = {Alexander Borisenko and Kostiantyn Drach},
journal= {arXiv preprint arXiv:1605.09157},
year = {2016}
}