2007/02/28 by Daniel A. Klain, Klain, Daniel A.
Mathematics · #52A22 #52A55 #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Morphological variations and asymmetry #Point processes and geometric inequalities #math.MG #msc:52A22 #msc:52A55
paper · pdf · doi:10.48550/arxiv.math/0702897
Latex, 11 pages
arxiv created 2007/02/28 · openalex publication_date 2007/02/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.