%0 Journal Article
%T Inequalities for Widths of Convex Bodies with Applications<br>凸体的宽度不等式及应用
%A Yuan Shufeng
%A Ke Rui
%A Leng Gangsong
%A <br>袁淑峰
%A 柯睿
%A 冷岗松
%J 数学物理学报(A辑)
%D 2007
%I 
%X 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$$w(\Omega)\ge r_n\cdot\frac{{{\rm Vol}_n}(\Omega)}{\displaystyle\max_{1\le i\le n+1}(S_i)},$$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.
%K Convex body
%K Width
%K Simplex
%K Volume<br>凸体
%K 宽度
%K 单形
%K 体积.
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=45E56ED9809BC6FF9F01099093574425&yid=A732AF04DDA03BB3&vid=DB817633AA4F79B9&iid=E158A972A605785F&sid=36C49E1242CC2C7A&eid=66D0A4667FE1A38D&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=9