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
[ Fulltext-pdf (140 KB)] for subscribers only.