Publisher DOI: 10.1112/S0025579314000291
arXiv ID: 1310.4368v4
Title: Sharpening geometric inequalities using computable symmetry measures
Language: English
Authors: Brandenberg, René 
König, Stefan 
Keywords: Mathematics - Metric Geometry; Mathematics - Metric Geometry; Computer Science - Computational Geometry
Issue Date: 5-Dec-2014
Publisher: Cambridge University Press
Source: Mathematika 61 (3): 559-580 (2015-09)
Abstract (english): 
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.
URI: http://hdl.handle.net/11420/9511
ISSN: 2041-7942
Journal: Mathematika 
Institute: Mathematik E-10 
Document Type: Article
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