On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width

被引：10
|
作者：
Bezdek, K. [1 ]
Kiss, Gy. [2 ]
机构：
[1] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada
[2] Eotvos Lorand Univ, Dept Geometry, Math Inst, H-1117 Budapest, Hungary
来源：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2009年 / 52卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
almost smooth convex body; convex body of constant width; weakly neighbourly antipodal convex polytope; Illumination Conjecture; X-ray number; X-ray Conjecture; ILLUMINATION;
D O I：
10.4153/CMB-2009-037-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The X-ray numbers of some classes of convex bodies are investigated. In particular, we give a proof of the X-ray Conjecture as well as of the Illumination Conjecture for almost smooth convex bodies of any dimension and for convex bodies of constant width of dimensions 3, 4, 5 and 6.
引用
收藏
页码：342 / 348
页数：7
相关论文
共 50 条
  • [1] On convex bodies of constant width
    Bazylevych, L. E.
    Zarichnyi, M. M.
    [J]. TOPOLOGY AND ITS APPLICATIONS, 2006, 153 (11) : 1699 - 1704
  • [2] Convex bodies of constant width
    Polovinkin, ES
    [J]. DOKLADY MATHEMATICS, 2004, 70 (01) : 560 - 562
  • [3] Convex Bodies of Constant Width with Exponential Illumination Number
    Arman, Andrii
    Bondarenko, Andrii
    Prymak, Andriy
    [J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2024,
  • [4] Asymmetry of Convex Bodies of Constant Width
    Jin, HaiLin
    Guo, Qi
    [J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2012, 47 (02) : 415 - 423
  • [5] Hyperspaces of convex bodies of constant width
    Antonyan, Sergey A.
    Jonard-Perez, Natalia
    Juarez-Ordonez, Saul
    [J]. TOPOLOGY AND ITS APPLICATIONS, 2015, 196 : 347 - 361
  • [6] Asymmetry of Convex Bodies of Constant Width
    HaiLin Jin
    Qi Guo
    [J]. Discrete & Computational Geometry, 2012, 47 : 415 - 423
  • [7] Convex bodies of constant width and constant brightness
    Howard, R
    [J]. ADVANCES IN MATHEMATICS, 2006, 204 (01) : 241 - 261
  • [8] Constant diameter and constant width of spherical convex bodies
    Han, Huhe
    Wu, Denghui
    [J]. AEQUATIONES MATHEMATICAE, 2021, 95 (01) : 167 - 174
  • [9] Constant diameter and constant width of spherical convex bodies
    Huhe Han
    Denghui Wu
    [J]. Aequationes mathematicae, 2021, 95 : 167 - 174
  • [10] Width of convex bodies in spaces of constant curvature
    Gallego, E.
    Reventos, A.
    Solanes, G.
    Teufel, E.
    [J]. MANUSCRIPTA MATHEMATICA, 2008, 126 (01) : 115 - 134
12345