关于内接单形的不等式及其应用

Geometric Inequalities And Their Applications For Inscribed Simplex

应用解析方法和几何不等式理论研究了n维欧氏空间E^n中涉及n维单形Ω_n与其内接单形Ω′_n的几何不等式的问题,建立了涉及单形Ω_n及其内接单形Ω′_n的外接球半径与高线的一类几何不等式,作为其特例得到了著名的n维Euler不等式的一些推广.

Using analytic method and theory of geometric inequality, we study the problem of geometric inequalities concerning n-dimensional simplex Ωn and its inscribed simplex Ω′n in E^n.Some geometric inequalities for the circumradius of Ωn and Ω′n and altitude are established.As the special case, some generalizations of the famous n-dimensional Euler inequality were obtained.