关于n维单形内点的几何不等式

Geometric Inequalities for an Interior Point of a Simplex

利用解析方法和几何不等式理论,研究了有关n维单形内点的几何不等式问题,建立了n维欧氏空间En中关于n维单形内点的一类几何不等式,作为其特例,得到了n维单形体积分别与其中线和外接球半径的几何不等式。

Using analytic method and theory of geometric inequality, the problem of geometric inequalities concerning an interior point of a simplex in EN is discussed, and some inequalities for an interior point of a simplex are established. As a special case, some geometric inequalities for volume of a simplex with its medians and circumradius are obtained.