| 凸体的宽度不等式及应用 |
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| 引用本文： | 袁淑峰,柯睿,冷岗松. 凸体的宽度不等式及应用[J]. 数学物理学报(A辑), 2007, 27(4): 660-664 |
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| 作者姓名： | 袁淑峰 柯睿 冷岗松 |
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| 作者单位： | 绍兴文理学院上虞分院数学系，上海大学数学系，上海大学数学系 上虞 312300 上海大学数学系 上海 200436，上海 200436，上海 200436 |
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| 摘 要： | 该文建立了关于单形宽度的杨路、张景中不等式的一个逆不等式. 作为凸体宽度不等式的应用,得到了凸体的截面和投影的一些估计式.
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| 关 键 词： | 凸体 宽度 单形 体积 |
| 文章编号： | 1003-3998（2007）04-660-05 |
| 收稿时间： | 2005-08-23 |
| 修稿时间： | 2005-08-23 |
Inequalities for Widths of Convex Bodies with Applications |
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| Yuan Shufeng,Ke Rui,Leng Gangsong. Inequalities for Widths of Convex Bodies with Applications[J]. Acta Mathematica Scientia, 2007, 27(4): 660-664 |
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| Authors: | Yuan Shufeng Ke Rui Leng Gangsong |
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| Affiliation: | 1 Department of Mathematics, Shangyu College Shaoxing University, Shaoxing 312300; 2Department of Mathematics, Shanghai University, Shanghai 200436 |
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| Abstract: | In this paper the authors establish the following inverse inequality of Yang-Zhang's inequality for the width of a simplex: Let $Omega$ be an n-dimensional simplex with volume Voln(Omega)$,width $w(Omega)$, and facet areas $S_1,S_2,cdots,S_{n+1}$ respectively, then$$w(Omega)ge r_ncdotfrac{{{rm Vol}_n}(Omega)}{displaystylemax_{1le ile n+1}(S_i)},$$where $$gamma_n=left{begin{array}{cl}disp frac{2n}{n+1}, & qquad {rm for~ odd}~~ n;2, & qquad {rm for~ even}~~ n.end{array} right.$$As applications, the authors show some inequalities for orthogonal projections and sections of convex bodies. |
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| Keywords: | Convex body Width Simplex Volume. |
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