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Bonnesen-type inequalities for surfaces of constant curvature

Daniel A. Klain
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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.

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Daniel A. Klain. 2007-02-28. Bonnesen-type inequalities for surfaces of constant curvature. https://arxiv.org/abs/math/0702897

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