相交体的凸性研究及Busemann定理的一点注记

Busemann定理表明一个关于原点对称凸体的相交体也是凸的．考虑Busemann定理是否对一般的少凸体也成立，并证明一个对称p-凸体的相交体对于某些给定的q而言是q-凸的；同时，推广一个Busemann定理，并应用它得到相交体的对偶Brunn-Minkowski不等式．

A research on the convexity of intersection bodies and some notes on Busemann theorem

Busemann theorem stated that the intersection body of an origin-symmetric convex body was also convex. In this paper, we provided a version of Busemann＇s theorem for general/〉convex bodies. It showed that the intersection body of a syrrmaetric p-convex body was q-convex for certain q. Meanwhile, we generalized a Busemann＇s theorerrL As an application, we got the dual Brunn-Minkowski inequality of the intersection bodies.