Sharpening geometric inequalities using computable symmetry measures

Publikationstyp
Journal Article
Date Issued
2014-12-05
Sprache
English
Author(s)
Brandenberg, René  
König, Stefan  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/9511
Journal
Mathematika  
Volume
61
Issue
3
Start Page
559
End Page
580
Citation
Mathematika 61 (3): 559-580 (2015-09)
Publisher DOI
10.1112/S0025579314000291
Scopus ID
2-s2.0-84948113105
ArXiv ID
1310.4368v4
Publisher
Cambridge University Press
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.
Subjects
Mathematics - Metric Geometry
Mathematics - Metric Geometry
Computer Science - Computational Geometry
DDC Class
510: Mathematik