The Illumination Conjecture for Spindle Convex Bodies

被引：1
作者：
Bezdek, Karoly [1 ,2 ,3 ]
机构：
[1] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada
[2] Univ Pannonia, Dept Math, H-8200 Veszprem, Hungary
[3] Eotvos Lorand Univ, Inst Math, H-1117 Budapest, Hungary
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2011年 / 275卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
CONSTANT WIDTH; HYPERBOLIC SPACES;
D O I：
10.1134/S0081543811080116
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls. A spindle convex body is called a "fat" one if it contains the centers of its generating balls. The main result of this paper is a proof of the illumination conjecture for "fat" spindle convex bodies in dimensions greater than or equal to 15.
引用
收藏
页码：169 / 176
页数：8
相关论文
共 14 条
  • [1] AIGNER M., 2010, Proofs from THE BOOK, V4th
  • [2] [Anonymous], 1911, Vierteljahrsschr. Nat.forsch. Ges. Zur.
  • [3] On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width
    Bezdek, K.
    Kiss, Gy.
    [J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2009, 52 (03): : 342 - 348
  • [4] BEZDEK K., 2006, PERIOD MATH HUNGAR, V53, P59
  • [5] Ball-polyhedra
    Bezdek, Karoly
    Langi, Zsolt
    Naszodi, Marton
    Papez, Peter
    [J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2007, 38 (02) : 201 - 230
  • [6] Boltyanski V., 1960, IZV MOLD FIL AKAD NA, V76, P77
  • [7] Boltyanskii V, 1980, DECOMPOSITION FIGURE
  • [8] COMPLETENESS AND CONSTANT WIDTH IN SPHERICAL AND HYPERBOLIC SPACES
    DEKSTER, BV
    [J]. ACTA MATHEMATICA HUNGARICA, 1995, 67 (04) : 289 - 300
  • [9] THE JUNG THEOREM FOR SPHERICAL AND HYPERBOLIC SPACES
    DEKSTER, BV
    [J]. ACTA MATHEMATICA HUNGARICA, 1995, 67 (04) : 315 - 331
  • [10] Transition from spherical circle packing to covering: Geometrical analogues of chemical isomerization
    Fowler, PW
    Tarnai, T
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1996, 452 (1952): : 2043 - 2064
12