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

Bernardo González Merino

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Bernardo González Merino

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

bg.merino@tum.de

Keywords

Inner and outer radii
Perel'man-Pukhov inequality
Section and projection
Jung's inequality
Steinhagen's inequality

Mathematics Subject Classification

52A20; 52A40

Suggested citation

B. González Merino. “Improving Bounds for the Perel'man-Pukhov Quotient for Inner and Outer Radii.” Journal of Convex Analysis 24 (2017), No. 4, 1099–1116.