Revista Matemática Iberoamericana
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Published online: 2007-12-31
Optimizing geometric measures for fixed minimal annulus and inradiusMaría A. Hernández Cifre and Pedro J. Herrero Piñeyro (1) Universidad de Murcia, Spain
(2) Universidad de Murcia, Spain
In this paper we relate the minimal annulus of a planar convex body $K$ with its inradius, obtaining all the upper and lower bounds, in terms of these quantities, for the classic geometric measures associated with the set: area, perimeter, diameter, minimal width and circumradius. We prove the optimal inequalities for each one of those problems, determining also its corresponding extremal sets.
Keywords: Convex bodies, minimal annulus, inradius, area, perimeter, circumradius, diameter, minimal width
Hernández Cifre María, Herrero Piñeyro Pedro: Optimizing geometric measures for fixed minimal annulus and inradius. Rev. Mat. Iberoam. 23 (2007), 953-971. doi: 10.4171/RMI/520