中文摘要：

1988年，Lutwak首次明确地提出了经典相交体的概念．2005年，Haberl和Ludwig对经典相交体进行了推广，给出了Lp-相交体的概念．最近，汪卫等提出了广义相交体的概念．主要利用Lp—Brunn—Minkowski理论、Holder积分不等式和Minkowski积分不等式，研究了广义相交体的单调性，并建立了关于径向线性组合和Lp-调和Blaschke组合的Brunn-Minkowski型不等式．

英文摘要：

In 1988, Lutwak first introduced the concept of intersection bodies. In 2005, Haberl and Ludwig extended the concept by introducing the concept of Lp- intersection bodies. Recently, Wang, et al. introduced the concept of generalized intersection bodies. This paper uses the Lp-Brunn-Minkowski theory, the HSlder integral inequality, and the Minkowski integral inequality to study the monotonicity of generalized intersection bodies, and establishes some Brunn-Minkowski inequal- ities about the radial linear combination and the Lp-harmonic Blaschke combina- tion.