关于单形宽度的Sallee猜想的加强

Improvement of Sallee's conjecture on the width of a simplex

文章利用几何不等式理论和解析的方法,研究了En中n维单形的宽度问题,给出了著名的Sallee猜想及其宽度与体积之间的不等式的一些加强,得到了关于单形宽度与外接球半径及单形体积之间更强的几个不等式。

Using the theory of geometric inequality and analytic method,the width of a n-dimensional simplex in En is studied and some improvements of Sallee＇s conjecture and the inequality between the width and volume are put forward.Then some improved inequalities between the simplex width,circumradius and simplex volume are obtained.