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SHARPENING GEOMETRIC INEQUALITIES USING COMPUTABLE SYMMETRY MEASURES

Part of: General convexity

Published online by Cambridge University Press:  05 December 2014

René Brandenberg  and
Stefan König
René Brandenberg
Affiliation:
Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany email brandenb@ma.tum.de
Stefan König
Affiliation:
Institut für Mathematik, Technische Universität Hamburg-Harburg, Schwarzenbergstr. 95, 21073 Hamburg, Germany email stefan.koenig@tuhh.de

Abstract

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Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the convex body. Since these coefficients are bounded by the dimension but possibly smaller, our inequalities sharpen the original ones. Since they can often be computed efficiently, the improved bounds may also be used to obtain better bounds in approximation algorithms.

MSC classification

Primary: 52A40: Inequalities and extremum problems

Information

Type
Research Article
Information
Mathematika , Volume 61 , Issue 3 , September 2015 , pp. 559 - 580
Copyright
Copyright © University College London 2014 

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