| 关于单形几个几何不等式的稳定性 |
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| 引用本文： | 杨世国,王文,齐继兵,钱娣. 关于单形几个几何不等式的稳定性[J]. 浙江大学学报(理学版), 2012, 39(1): 12-17 |
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| 作者姓名： | 杨世国 王文 齐继兵 钱娣 |
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| 作者单位： | 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 |
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| 基金项目： | 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) |
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| 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.
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| 关 键 词： | euclidean空间 单形 宽度 中线 中面 稳定性 |
The stability of some geometric inequalities for a simplex |
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| YANG Shi-guo , WANG Wen , QI Ji-bing , QIAN Di. The stability of some geometric inequalities for a simplex[J]. Journal of Zhejiang University(Sciences Edition), 2012, 39(1): 12-17 |
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| Authors: | YANG Shi-guo WANG Wen QI Ji-bing QIAN Di |
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| Affiliation: | 1.Department of Mathematics and Teacher Education Research Center,Hefei Normal University,Hefei 230061,China;2.School of Mathematical Sciences,Anhui University,Hefei 230039,China) |
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| Abstract: | 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. |
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| Keywords: | Euclidean space simplex width median middle section stability |
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