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中文摘要：
利用距离几何的理论与方法,研究了球面空间S_n（K）中n维单形的几何不等式问题,建立了涉及n维球面单形体积、外接球半径、内切球半径与棱长的几个几何不等式,这些几何不等式是球面单形几何不等式研究的基础.
英文摘要：
In this paper,we study the problem on geometric inequalities for an n-dimensional simplex in the spherical space S_n（k） by using the theory and method of metric geometry.Some geometric inequalities for the volume,the radius of circumscribed and inscribed sphere and as well as edge-lengths of an n-dimensional simplex in the spherical space are established.These geometric inequalities are the base of reseach for studying inequalities of spherical simplices.
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