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| 摘要: |
| 本文应用距离几何的理论与方法,研究了n维球面空间中n维单形与有限点集的几何不等式问题,建立了球面空间中n维单形一种形式的Pedoe不等式与有限点集一种形式的张-杨不等式,并应用它获得n维球面空间中Veljan-Korchmaros型不等式与Finsler-Hadwinger型不等式. |
| 关键词: 球面空间 单形 有限点集 几何不等式 |
| DOI： |
| 分类号:O184 |
| 基金项目:国家自然科学基金(60671051)资助项目;高等学校博士学科点专项科研基金项目(20113401110009);安徽省高等学校自然科学基金项目(KJ2011B133). |
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| THE PEDOE INEQUALITY AND ZHANG-YANG INEQUALITY IN THE SPHERICAL SPACE WITH APPLICATIONS |
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YANG Shi-guo,QI Ji-bing,WANG Wen
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| Abstract: |
| In this paper, we study the problems about geometric inequalities for ndimensional simplexes and finite point sets in the n-dimensional spherical space by theory and method of distance geometry. A form of Pedoe inequality for n-dimensional simplexes and a form of Zhang-Yang inequality for finite point sets in the spherical space are established. From this we obtain the Veljan-Korchmaros inequality and the Finsler-Hadwinger inequality in the n-dimensional spherical space. |
| Key words: spherical space simplex finite point sets geometric inequality |
