Modified Busemann-Petty problem on sections of convex bodies

被引：13

作者：

Koldobsky, A. ^{[1
]}

Yaskin, V. ^{[1
]}

Yaskina, M. ^{[1
]}

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2006年 / 154卷 / 1期

基金：

美国国家科学基金会;

关键词：

Convex Body; Fractional Derivative; Homogeneous Function; Positive Real Root; Section Function;

D O I：

10.1007/BF02773605

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Busemann-Petty problem asks whether convex origin-symmetric bodies in R-n with smaller central hyperplane sections necessarily have smaller n-dimensional volume. It is known that the answer is affirmative if n <= 4 and negative if n >= 5. In this article we replace the assumptions of the original Busemann-Petty problem by certain conditions on the volumes of central hyperplane sections so that the answer becomes affirmative in all dimensions.

引用

页码：191 / 207

页数：17

共 16 条

[1]

Bourgain J., 1999, MATH SCI RES I PUBL, V34, P65

[2]

Busemann H., 1956, MATH SCAND, V4, P88

[3] An analytic solution to the Busemann-Petty problem on sections of convex bodies [J].