Revista Matemática Iberoamericana

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Volume 23, Issue 3, 2007, pp. 953–971
DOI: 10.4171/RMI/520

Published online: 2007-12-31

Optimizing geometric measures for fixed minimal annulus and inradius

María A. Hernández Cifre[1] and Pedro J. Herrero Piñeyro[2]

(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