双曲空间中Veljan-Korchmaros型不等式及应用

摘要

本文研究了双曲空间Hn(K)中n维高维单形的几何不等式问题.利用距离几何的理论与方法,获得了涉及n维双曲单形体积,侧面积与棱长的几个几何不等式,这些几何不等式是双曲单形几何不等式的基础.%In this paper, we study the problem about geometric inequalities for an n-dimensional simplex in the hyperbolic space Hn(K). By using the theory and method of distance geometry, some geometric inequalities for volume, edge-lengths of an n-dimensional simplex in the Hyperbolic space are established, which are the base of research of geometric inequalities for hyperbolic simplices.