混合投影体的极与混合相交体的Aleksandrov-Fenchel 不等式的稳定性

数学物理学报 ›› 2009, Vol. 29 ›› Issue (6): 1750-1764.

混合投影体的极与混合相交体的Aleksandrov-Fenchel 不等式的稳定性

河西学院数学系甘肃张掖 734000

收稿日期:2007-11-23 修回日期:2008-12-22 出版日期:2009-12-25 发布日期:2009-12-25
基金资助:
国家自然科学基金(10971128)和甘肃省教育厅科研基金(0709-03)资助

The Stability of Aleksandrov-Fenchel Inequality for Polars of Mixed Projection Bodies |and Mixed Intersection Bodies

Department of Mathematics, Hexi University, Gansu |Zhangye |734000

Received:2007-11-23 Revised:2008-12-22 Online:2009-12-25 Published:2009-12-25
Supported by:
国家自然科学基金(10971128)和甘肃省教育厅科研基金(0709-03)资助

摘要/Abstract

摘要：

引进了多个几何体(主要是凸体(Convex body)和星体(Star body)) 相似``偏差''的一个度量方法, 从而推广了已有的相似``偏差''度量方法.并在此度量下, 利用Rⁿ 中Hölder不等式的一个加强获得了文献[1]建立的混合投影体的极的Aleksandrov-Fenchel不等式和文献[2]建立的混合相交体的Aleksandrov-Fenchel不等式的稳定性版本.

关键词: 凸体, 星体, 混合投影体, 混合相交体, 混合投影体的极

Abstract:

A metric method for homothetic deviation of m(m ≥ 2) geometirc bodies(star bodies or convex bodies) is provided. By the metric mthod, and utilizing a refinement of Hölder inequality the author establishes a stablity version of Aleksandrov-Fenchel inequality for polars of mixed projection bodies and mixed intersection bodies.

Key words: Convex body, Star body, Mixed projection body, Mixed intersection body, Polar of mixed projection body

中图分类号:

52A40

马统一. 混合投影体的极与混合相交体的Aleksandrov-Fenchel 不等式的稳定性[J]. 数学物理学报, 2009, 29(6): 1750-1764.

MA Tong-Yi. The Stability of Aleksandrov-Fenchel Inequality for Polars of Mixed Projection Bodies |and Mixed Intersection Bodies[J]. Acta mathematica scientia,Series A, 2009, 29(6): 1750-1764.

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