Convex bodies of constant width and constant brightness

被引：15
作者：
Howard, R [1 ]
机构：
[1] Univ S Carolina, Dept Math, Columbia, SC 29208 USA
来源：
ADVANCES IN MATHEMATICS | 2006年 / 204卷 / 01期
关键词：
Nakajima problems; constant width; constant brightness; regularity of support functions; relative geometry; quasiregular maps;
D O I：
10.1016/j.aim.2005.05.015
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In 1926 Nakajima (=Matsumura) showed that any convex body in R-3 with constant width, constant brightness, and boundary of class C-2 is a ball. We show that the regularity assumption on the boundary is unnecessary, so that balls are the only convex bodies of constant width and brightness. (C) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：241 / 261
页数：21
相关论文
共 23 条
[1]  
[Anonymous], ENCY MATH ITS APPL
[2]  
[Anonymous], 1995, ENCY MATH ITS APPL
[3]  
[Anonymous], 1993, ERGEBNISSE MATH IHRE
[4]  
Bonnesen T., 1971, THEORIE KONVEXEN KOR
[5]  
Chakerian G.D., 1983, CONVEXITY ITS APPL, P49
[6]   SETS OF CONSTANT RELATIVE WIDTH AND CONSTANT RELATIVE BRIGHTNESS [J].
CHAKERIAN, GD .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 129 (01) :26-+
[7]   IS A BODY SPHERICAL IF ALL ITS PROJECTIONS HAVE SAME IQ [J].
CHAKERIAN, GD .
AMERICAN MATHEMATICAL MONTHLY, 1970, 77 (09) :989-+
[8]  
Clarke F.H., 1990, OPTIMIZATION NONSMOO
[9]  
CROFT HT, 1991, UNSOLVED PROBLEMS IN, V2
[10]  
Federer H., 1969, GEOMETRIC MEASURE TH
123