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.
出处
《浙江大学学报（理学版）》
CAS
CSCD
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)
