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Busemann-Petty问题及其相关研究综述
  • ISSN号：1000-0917
  • 期刊名称：数学进展
  • 时间：0
  • 页码：596-603
  • 语言：中文
  • 分类：O184[理学—数学;理学—基础数学]
  • 作者机构：[1]上海大学数学系,上海200444, [2]重庆师范大学数学系,重庆400047
  • 相关基金：国家自然科学基金（No.10671117）.
  • 相关项目：Lp空间中的凸体极值问题
作者： 冷岗松|吕松军|
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
中文摘要：

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.

英文摘要：

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.

同期刊论文项目
Lp空间中的凸体极值问题
期刊论文 52
同项目期刊论文
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On the Lp-version of the Petty's conjectured projection inequality and applications
L_p-投影体的均质积分和对偶均质积分的Brunn-Minkowski不等式
On dual quermassintegrals of mixed intersection bodies
Some affine isoperimetric inequalities associated with L-p(-) affine surface area
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On a Heilbronn-type problem
ON L-p-BRUNN-MINKOWSKI TYPE INEQUALITIES OF CONVEX BODIES
A generalization of the matrix form of the Brunn-Minkowski inequality
Inequalities for L-p centroid body
On the L-p intersection body
Dual L-p John ellipsoids
Cross i-sections of star bodies and dual mixed volumes
凸体的宽度不等式及应用
对偶L_p-质心体与Fourier变换
Loomis-Whitney's inequality about mixed body
Volume inequalities for L-p-John ellipsoids and their duals
L-p-dual mixed quermassintegrals (vol 36, pg 177, 2005)
The p-affine surface area
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Inequalities relating to L-p -version of Petty's conjectured projection inequality
凸几何经典不等式的蕴含关系
关于广义Busemann-Petty问题
Quasi L-p-Intersection bodies
The petty projection inequality for L-p-mixed projection bodies
Inequalities for star duals of intersection bodies
On the generalized Busemann-Petty problem
p-完美凸集和绝对p-完美凸集
Marcinkiwicz算子的多线性交换子在一类Block—Hardy空间上的加权有界性
On Isolations for the Brunn-Minkowski Inequality of Quermassintegrals and Dual Quermassintegrals
On Reverses of the Lp-petty Projection Inequality
On Reverses of the Blaschke-Santalo Inequality for Convex Bodies
凸二次整数规划的随机水平值逼近算法
凸体的P-宽度积分
联系投影不等式Petty猜想的Lp-形式的不等式
Veljan-Korchmaros型不等式的稳定性
Lp-对偶几何表面积
Inequalities relating to Lp-version of Petty＇s conjectured projection inequality
On the Lp intersection body
拟Lp-混合相交体
Inequalities for the Radial p-th Mean Bodies
On Reverses of the L_p-Busemann-Petty Centroid Inequality and Its Applications
Several inequalities for L2-projection body
Isotropic dual p-surface area measure
Some Inequalities for the Lp-Mixed Quermassintegrals
Inequalities for pedal simplices
p-截面体的性质与推广
Some properties of mixed radial mean bodies on integral transform
Several properties of new ellipsoids
期刊信息
  • 《数学进展》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学协术学会
  • 主办单位:中国数学会
  • 主编：丁伟岳
  • 地址：北京大学数学系数学进展编辑部
  • 邮编：100871
  • 邮箱：
  • 电话：
  • 国际标准刊号：ISSN：1000-0917
  • 国内统一刊号：ISSN：11-2312/O1
  • 邮发代号:2-503
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:3411