n维欧氏空间E^n中Child不等式的推广

Extensions of Child Inequality for n-dimensional Simplex in E^n

利用几何不等式理论与解析方法,研究了n维欧氏空间En中n维单形的内点到各顶点的距离与到各侧面距离之间的关系,获得相关的几个几何不等式,推广了Child不等式.

Using analytic method and theory of geometric inequalities, The problem about geometric inequalities for an interior point of a simplex was given. A class of geometric inequalities for an interior point of a simplex are established. The n-dimensional Child inequality was improved.