SHARPENING GEOMETRIC INEQUALITIES USING COMPUTABLE SYMMETRY MEASURES

被引：13
作者：
Brandenberg, Rene [1 ]
Koenig, Stefan [2 ]
机构：
[1] Tech Univ Munich, Zentrum Math, D-85747 Garching, Germany
[2] Tech Univ Hamburg, Inst Math, D-21073 Hamburg, Germany
来源：
MATHEMATIKA | 2015年 / 61卷 / 03期
关键词：
OUTER J-RADII; CONVEX; COMPLEXITY; CONTAINMENT; POLYTOPES; VOLUME; INNER; SETS;
D O I：
10.1112/S0025579314000291
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：559 / 580
页数：22
相关论文
共 44 条
  • [1] [Anonymous], 1922, Abh. Math. Semin. Univ. Hambg.
  • [2] [Anonymous], 1993, Convex Bodies: The Brunn-Minkowski Theory
  • [3] BALL K, 1992, GEOMETRIAE DEDICATA, V41, P241
  • [4] Ball K, 1997, Flavors of geometry, V31, P1
  • [5] On the symmetry function of a convex set
    Belloni, Alexandre
    Freund, Robert M.
    [J]. MATHEMATICAL PROGRAMMING, 2008, 111 (1-2) : 57 - 93
  • [6] ESTIMATING SIZES OF A CONVEX BODY BY SUCCESSIVE DIAMETERS AND WIDTHS
    BETKE, U
    HENK, M
    [J]. MATHEMATIKA, 1992, 39 (78) : 247 - 257
  • [7] Jung's theorem for a pair of Minkowski spaces
    Boltyanski, Vladimir
    Martini, Horst
    [J]. ADVANCES IN GEOMETRY, 2006, 6 (04) : 645 - 650
  • [8] Bonnesen T, 1987, THEORY CONVEX BODIES
  • [9] Optimizing area and perimeter of convex sets for fixed circumradius and inradius
    Boroczky, K
    Cifre, MAH
    Salinas, G
    [J]. MONATSHEFTE FUR MATHEMATIK, 2003, 138 (02): : 95 - 110
  • [10] Bottema O., 1969, Geometric Inequalities, V1st ed.
12345