欧氏空间E^n中k-n型Pedoe不等式的推广及应用

GENERALIZATIONS OF THE k-n TYPE NEUBERG-PEDOE INEQUALITY IN THE EUCLIDEAN SPACE E^n WITH APPLICATIONS

利用距离几何的理论与方法,研究欧氏空间E^n中涉及两个单形体积的几何不等式问题,建立了涉及两个单行体积的几个不等式,推广了n维单形的k-n型Pedoe不等式与k-n型彭—常不等式.

In this paper,using the theory and method of distance geometry we study the problems of geometry inequalities for the volumes of two simplexes in the Euclidean Space En.Some geometric inequalities for the volumes of two simplexes are established.The k-n type Pedoe inequality and the k-n type Peng-Chang inequality for n-dimensional simplexes are improved.