A COMPLETE 3-DIMENSIONAL BLASCHKE-SANTALO DIAGRAM

被引：6
作者：
Brandenberg, Rene [1 ]
Merino, Bernardo Gonzalez [1 ]
机构：
[1] Tech Univ Munich, Zentrum Math, Boltzmannstr 3, D-85747 Garching, Germany
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2017年 / 20卷 / 02期
关键词：
Inradius; circumradius; geometric inequalities; Blaschke diagram; Blaschke-Santalo diagram; shape diagrams; CONVEX-SETS; PERIMETER; DIAMETER; WIDTH; AREA;
D O I：
10.7153/mia-20-22
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present a complete 3-dimensional Blaschke-Santalo diagram for planar convex bodies with respect to the four classical magnitudes: inradius, circumradius, diameter, and (minimal) width in Euclidean spaces.
引用
收藏
页码：301 / 348
页数：48
相关论文
共 24 条
  • [1] [Anonymous], 1916, Jahresber. Deutsch. Math. Ver
  • [2] [Anonymous], 1961, Math. Notae
  • [3] Bonnesen T., 1974, THEORIE KONVEXEN KOR
  • [4] Bonnesen T., 1934, Theory of convex bodies
  • [5] 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
  • [6] SHARPENING GEOMETRIC INEQUALITIES USING COMPUTABLE SYMMETRY MEASURES
    Brandenberg, Rene
    Koenig, Stefan
    [J]. MATHEMATIKA, 2015, 61 (03) : 559 - 580
  • [7] No Dimension-Independent Core-Sets for Containment Under Homothetics
    Brandenberg, Rene
    Koenig, Stefan
    [J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2013, 49 (01) : 3 - 21
  • [8] Cifre MAH, 2000, DISCRETE COMPUT GEOM, V23, P381, DOI 10.1007/s004540010006
  • [9] Cifre MAH, 2002, ARCH MATH, V79, P147
  • [10] Is there a planar convex set with given width, diameter, and inradius?
    Cifre, MAH
    [J]. AMERICAN MATHEMATICAL MONTHLY, 2000, 107 (10) : 893 - 900
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