关于k个单形的一类几何不等式

A Class of Geometric Inequalities Concerning K Simplexes

本文证明了涉及k个单形的一类几何不等式,并进一步得到了一些有用的推论。

In this paper, the inequalities involving K Simplexes are proved:Where a_((i)_j)、V_i and r_i are the edge—lengthr、Volume and inradius of n—Simplex ∑_A, in E^n. And the equality holds if and only if the simplex ∑_A, is regular (i=1, 2,…, k), (j=1, 2,…,(n(n+1))/2), a∈R.