凸体几何中几个猜想的等价性

上海大学学报(自然科学版) ›› 2010, Vol. 16 ›› Issue (3): 257-261.

凸体几何中几个猜想的等价性

柏世松,何斌吾

(上海大学理学院，上海 200444)

出版日期:2010-06-28 发布日期:2010-06-28

Equivalence of Several Conjectures for Convex Geometry

BO Shi-song,HE Bin-wu

(College of Sciences, Shanghai University, Shanghai 200444, China)

Online:2010-06-28 Published:2010-06-28

摘要/Abstract

摘要：

凸体几何是以凸体或星体为主要研究对象的现代几何学的一个重要分支,其中有许多未解决的问题和猜想,许多猜想看似不同而事实上是等价的. 证明了“迷向常数猜想”、“截片问题”、“BusemannPetty猜想”和“逆BrunnMinkowski不等式”等问题的等价性. 

关键词: 凸体;迷向体;迷向常数;超平面截面

Abstract:

Convex geometry is an important branch of modern geometry. Convex bodies and star bodies are a main object of study with many unsolved open problems and conjectures. Although these problems and conjectures are different, they are actually equivalent. In this paper, we discuss the connection of several conjectures such as isotropic constant conjecture, slicing problem, Busemann-Petty problem, and reverse Brunn-Minkowski inequality. We give proofs of the equivalence.

Key words: convex body; isotropic body; isotropic constant; hyperplane section

柏世松,何斌吾. 凸体几何中几个猜想的等价性[J]. 上海大学学报(自然科学版), 2010, 16(3): 257-261.

BO Shi-song,HE Bin-wu. Equivalence of Several Conjectures for Convex Geometry[J]. Journal of Shanghai University（Natural Science Edition）, 2010, 16(3): 257-261.