关于n维Euler不等式的再改进

Further improvement of Euler inequality

本文主要运用代数方法和几何不等式理论,研究了有关单形中Euler不等式的高维推广和改进的问题。建立了涉及单形Ωn及其内接单形Ω′n的外接球半径以及Ωn中内点到各侧面距离之间的几何不等式。作为特例,对n维Euler不等式作了新的推广和改进。

In this thesis,by using analytic method and theory of geometric inequality,conjecture and improvement of n-dimension Euler inequality are researched.A geometric inequality for the circumradius of Ωn and Ωn' and distance of interior point to side faces of Ωn is established,which is new improvement of Euler inequality as application.