关于单形几个几何不等式的稳定性  

The stability of some geometric inequalities for a simplex

作　　者：杨世国[1] 王文[1] 齐继兵[1] 钱娣[2] 

机构地区：[1]合肥师范学院数学系和教师教育研究中心,安徽合肥230061 [2]安徽大学数学科学学院,安徽合肥230039

出　　处：《浙江大学学报（理学版）》2012年第1期12-17,共6页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(60671051);安徽省高校省级重点项目(KJ2009A45)

摘　　要：利用度量几何的理论与方法研究了n维欧氏空间En中n维单形几个几何不等式的稳定性,从2个单形偏正度量证明了n维单形宽度的Sallee-Alexander不等式与杨-张不等式是稳定的;证明了n维单形中线型与中面型Veljan-Korchmaros不等式是稳定的.并给出了单形的几何不等式的稳定性版本,从而推广了这类几何不等式.Using the theory and methods of metric geometry to study the problems of stability,which is some geometric inequalities for an n-simplex in the n-dimensional Euclidean space En.From the deviation regular metric of two simplexes,we prove that Sallee-Alexander's and Yang-Zhang's inequalities for the width of an n-simplex are all stable,and also prove that Veljan-Korchmaros's inequalities for the medians and the middle sections of an n-simplex are all stable.The stability versions of these geometric inequalities for a simplex are established,and these geometric inequalities are improved.

关 键 词：EUCLIDEAN空间 单形 宽度 中线 中面 稳定性 

分 类 号：O178[理学—数学]