凸体几何中几个猜想的等价性

Equivalence of Several Conjectures for Convex Geometry

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.

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.