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Journal of Convex Analysis 24 (2017), No. 4, 1099--1116
Copyright Heldermann Verlag 2017

Improving Bounds for the Perel'man-Pukhov Quotient for Inner and Outer Radii

Bernardo González Merino
Zentrum Mathematik, Technische Universität, Boltzmannstr. 3, 85747 München - Garching, Germany

We study upper bounds for the ratio of successive inner and outer radii of a convex body K. This problem was studied by Perel'man and Pukhov and it is a natural generalization of the classical results of Jung and Steinhagen. We also introduce a technique which relates sections and projections of a convex body in an optimal way.

Keywords: Inner and outer radii, Perel'man-Pukhov inequality, Section and projection, Jung's inequality, Steinhagen's inequality.

MSC: 52A20; 52A40

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