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中文摘要：
对于p〈1和p≠0,Haberl和Ludwig引进了星体的L_p-截面体I_pK的概念.该文研究截面体的极值性质,获得了L_p-截面体的单调性,建立了L_p-Busemann-Petty截面不等式.并且将L_p-截面体的概念进一步拓展,提出了L_p-混合截面体的概念.作为应用,建立了L_p-混合截面体和它的极体的Aleksandrov-Fenchel型不等式.这些结果是已有结果的对偶形式.
英文摘要：
For p 〈 1 and p≠0,Haberl and Ludwig introduced an L_p-mterscction body I_PK of a star body K.In this paper we study extreme nature of the L_p-mtersection body,and L_p-type Busemann-Petty intersection inequality is established.Meanwhile,we further expand the concept of L_p-intersection body to L_p-mixed intersection body is put forward.As an application,we establish Aleksandrov-Fenchel type inequalities for L_p-mixed intersection body and its polar body.These results are the dual form of some known results.
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