关于单形的k-超切球的一些结果

Some Results of k-Tangent Sphere of Simplex

首先给出了n维单形的k-超切球的概念 ,它统一定义了n维单形的外接超球、棱切超球、…、内切超球 .获得了n维单形存在k-超切球的充分必要条件 .应用著名的度量方程 ,给出了k -超切球半径的计算公式 .将“弱度量加”运算用于存在k-超切球的单形中 ,获得了一类涉及n维单形体积和k-超切球半径的几何不等式 ,这些结果蕴含了文 [5,14,15。

In this paper, the definition of k-tangent sphere of n dimension simplex is given. It provides unified definitions of some tangent spheres of simlpex. The necessary and sufficient condition is obtained of n dimension simplex where k-tagent sphere exists. Then the k-tangent sphere and the faible metric addition to simplexes in which k-tangent sphere exists are applied, and a class of geometric inequalities are obtained, which include the main results in papers[5,14,15,19].