凸体体积比的相关性质被引量：1

Properties of Volume Ratios of Convex Bodies

下载PDF

导出

摘要讨论对称凸体的体积比与其截面、投影的体积比的关系,推出体积比的Blaschke-Santaló类型的不等式,以及得到超立方体的体积比和单形体积比的渐进性质. In this paper, relationship of volume ratios between a symmetric convex body and its sections and projections is shown. A Blaschke-Santaló type inequality on volume ratio is proved, and some asymptotic properties of volume ratios of cube and simplex are observed.

作者英起志冷岗松

机构地区上海大学理学院

出处《上海大学学报（自然科学版）》 CAS CSCD 北大核心 2008年第4期373-376,共4页 Journal of Shanghai University:Natural Science Edition

基金国家自然科学基金资助项目(10671117)

关键词凸体体积比不等式渐进性 convex body volume ratio inequality asymptotic property

分类号 O184 [理学—基础数学]

引文网络
相关文献

参考文献9

1BALL K M. Volumes of sections of cubes and related problems [ M]. Berlin: Springer LNM,1989,1376:251- 260.
2BALL K M. Volume ratios anti a reverse isoperimetric inequality [ J ]. Journal of the London Mathematical Society, 1991,44:351-359.
3BOURGAIN J, MILMAN V D. New volume ratio properties for convex symmetric bodies in R [ J ]. Invent Math, 1987, 88:319-340.
4BALL K M. Ellipsoid of maximal volume in convex bodies [J]. Geom Dedicata, 1992, 41:241-250.
5JOHN F. Extremum problems with inequalities as subsidiary conditions [ M ] // Courant Anniversary Volume. New York : Interscience, 1948 : 187-204.
6LUTWAK E, ZHANG G Y. Blaschke-Santalo inequalities [ J ]. J Differential Geometry, 1997,45 : 1- 16.
7LUTWAK E. The Brunn-Minkowski-Firey theory( I )- mixed volumes and the Minkowski problem [ J ]. J Differential Geom, 1993, 38 : 131-150.
8GARDNER R J. Geometric tomography [ M ]. Cambridge: Cambridge University Press, 1995:145- 149.
9SCHNEIDER R. Convex bodies: the Brunn-Minkowski theory [ M ]. Cambridge : Cambridge University Press, 1993:33-37.

同被引文献6

1张素玲,陈超平,祁锋.关于伽玛函数的单调性质(英文)[J].大学数学,2006,22(4):50-55. 被引量：6
2R Howard.The John ellipsoid theorem[J].University of South Carolina,1997.
3Keith Ball.Volume ratios and a reverse isoperimetric inequality[J].Journal of the London Mathematical Society,1991,44:351-359.
4Keith Ball.Ellipsoids of maximal volume in convex bodies[J].Geometriae Dedicata,1992,41:241-250.
5Keith Ball.Volumes of sections of cubes and related problems[J].Geometric Aspects of Functional Analysis,1989,1376:251-260.
6John F.Extremum problems with inequalities assubsidiary conditions[M].Courant Anniversary Volume.New York:Interscie nce,1948:187-204.

引证文献1

1英起志.n维超平形体的体积比[J].高教学刊,2016,2(22):253-253.

上海大学学报（自然科学版）

2008年第4期

浏览历史

内容加载中请稍等...

凸体体积比的相关性质被引量：1

参考文献9

同被引文献6

引证文献1

相关作者

相关机构

相关主题

浏览历史

凸体体积比的相关性质 被引量：1

参考文献9

同被引文献6

引证文献1

相关作者

相关机构

相关主题

浏览历史

凸体体积比的相关性质被引量：1