关于单形及内接单形的几何不等式及应用

Geometric Inequality and Applications for Simplex and Its Inscribed Simplex

运用代数方法和几何不等式理论,研究了有关单形内点及其内接单形的极值问题,建立了涉及单形及其内接单形的外接球半径以及内点到侧面距离之间的几何不等式.作为特例,对著名的n维Euler不等式作了新的推广和改进.

The extremum problem of simplex interior point and inscribed simplex is researched, by using analytic method and theory of geometric inequality. A geometric inequality for distance of interior point to side faces of simplex and for the circumradius of simplex and its inscribed simplex is established, which is new improvement of Euler inequality as application.