Bonnesen-type inequalities for surfaces of constant curvature
Metric Geometry
2007-05-23 v1
Abstract
A Bonnesen-type inequality is a sharp isoperimetric inequality that includes an error estimate in terms of inscribed and circumscribed regions. A kinematic technique is used to prove a Bonnesen-type inequality for the Euclidean sphere (having constant positive Gauss curvature) and the hyperbolic plane (having constant negative Gauss curvature). These generalized inequalities each converge to the classical Bonnesen-type inequality for the Euclidean plane as the curvature approaches zero.
Keywords
Cite
@article{arxiv.math/0702897,
title = {Bonnesen-type inequalities for surfaces of constant curvature},
author = {Daniel A. Klain},
journal= {arXiv preprint arXiv:math/0702897},
year = {2007}
}
Comments
Latex, 11 pages