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Busemann-Petty问题及其相关研究综述 被引量：2

Busemann-Petty Problem and Its Related Topics——A Survey
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摘要 Busemann-Petty问题是凸几何及其相关学科中的一个极其重要的问题.在近几十年解决这一问题的过程中,凸几何学的研究领域和研究方法得到了极大的丰富和发展.本文首先阐述了Busemann-Petty问题的历史,然后综述了与Busemann-Petty问题紧密相关的一些公开问题和重要课题的研究现状和最新的进展. Busemann-Petty problem is an important problem in Convex Geometry and its related subjects. The research area and approach of convex geometry have been enlarged and developed essentially during recent decades, in which the Busemann-Petty problem was solved completely. In this paper, we firstly recall the history of the Busemann-Petty problem, and then we give an overview of some famous open problems and some important topics associated closely to the Busemann-Petty problem. The new progress on these open problems and related topics are also presented in this survey paper.
作者 冷岗松 吕松军
机构地区 上海大学数学系 重庆师范大学数学系
出处 《数学进展》 CSCD 北大核心 2008年第5期513-526,共14页 Advances in Mathematics（China）
基金 国家自然科学基金(No.10671117).
关键词 凸体Busemann-Petty问题 截面体 广义Busemann-Petty问题 广义截面体 截面问题 convex body the Busemann-Petty problem intersection body the generalized Busemann-Petty problem the generalized intersection body the slicing problem
分类号 O184 [理学—基础数学]
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共引文献11

同被引文献39

  • 1HE Binwu & LENG Gangsong Department of Mathematics, Shanghai University, Shanghai 200444, China.Isotropic bodies and Bourgain's problem[J].Science China Mathematics,2005,48(5):666-679. 被引量：6
  • 2何斌吾,冷岗松.迷向体与Bourgain问题[J].中国科学（A辑）,2005,35(4):450-462. 被引量：12
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  • 8柏世松,何斌吾.凸体几何中几个猜想的等价性[J].上海大学:自然科学版,2010,16(3):257-261.
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数学进展
2008年 第5期

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