|Publisher DOI:||10.1112/S0025579314000291||arXiv ID:||1310.4368v4||Title:||Sharpening geometric inequalities using computable symmetry measures||Language:||English||Authors:||Brandenberg, René
|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|
|Appears in Collections:||Publications without fulltext|
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