Bonnesen-type inequalities for surfaces of constant curvature

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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.
Latex, 11 pages

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Metric Geometry, 52A55; 52A22

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http://salesiana.dossiersoluciones.com/handle/123456789/124838

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702897
 http://arxiv.org/abs/math/0702897

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arXiv