On the generalized Busemann-Petty problem

查看全文 作　　者：Song-jun L~(1,2+) Gang-song LENG~1 1.College of Mathematics and Computer Science,Chongqing Normal University,Chongqin 400047,China;2.Department of Mathematics,Shanghai University,Shanghai 200444,China

出　　处：《Science China Mathematics》索引2007年第50卷第8期,共14页

基　　金：the National Natural Science Foundation of China(Grant No.10671117) 摘　　要：The generalized Busemann-Petty problem asks whether the origin-symmetric convex bod- ies in R^n with a larger volume of all i-dimensional sections necessarily have a larger volume.As proved by Bourgaln and Zhang,the answer to this question is negative if i>3.The problem is still open for i=2,3.In this article we prove two specific affirmative answers to the generalized Busemann-Petty problem if the body with a smaller i-dimensional volume belongs to given classes.Our results generalize Zhang’s specific affirmative answer to the generalized Busemann-Petty problem. 关键词：STAR BODY CROSS I-SECTION dual mixed volume RADON TRANSFORM

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On the generalized Busemann-Petty problem

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