INTERSECTION BODIES AND THE BUSEMANN-PETTY PROBLEM

被引:134
作者
GARDNER, RJ
机构
关键词
CONVEX BODY; SECTION; BUSEMANN-PETTY PROBLEM; INTERSECTION BODY;
D O I
10.2307/2154703
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
It is proved that the answer to the Busemann-Petty problem concerning central sections of centrally symmetric convex bodies in d-dimensional Euclidean space E(d) is negative for a given d if and only if certain centrally symmetric convex bodies exist in E(d) which are not intersection bodies. It is also shown that a cylinder in E(d) is an intersection body if and only if d less-than-or-equal-to 4, and that suitably smooth axis-convex bodies of revolution are intersection bodies when d less-than-or-equal-to 4. These results show that the Busemann-Petty problem has a negative answer for d greater-than-or-equal-to 5 and a positive answer for d = 3 and d = 4 when the body with smaller sections is a body of revolution.
引用
收藏
页码:435 / 445
页数:11
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