Two Geometric Inequalities in Spherical Space

摘要

In this paper,by using the theory and method of distance geometry,we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length and volume of one simplex and the volume,height and (n-1)-dimensional volume of the side of another simplex in the n-dimensional spherical space.They are the extensions of the results [10] in the n-dimensional Euclidean geometry to the n-dimensional spherical space.