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中文摘要：
本文应用距离几何的理论与方法,研究了n维球面空间中n维单形与有限点集的几何不等式问题,建立了球面空间中n维单形一种形式的Pedoe不等式与有限点集一种形式的张-杨不等式,并应用它获得n维球面空间中Veljan-Korchmaros型不等式与Finsler-Hadwinger型不等式.
英文摘要：
In this paper, we study the problems about geometric inequalities for n- dimensional simplexes and finite point sets in the n-dimensional spherical space by theory and method of distance geometry. A form of Pedoe inequality for n-dimensional simplexes and a form of Zhang-Yang inequality for finite point sets in the spherical space are established. From this we obtain the Veljan-Korchmaros inequality and the Finsler-Hadwinger inequality in the n-dimensional spherical space.
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