English

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}
}