极性理论应用于几何不等式

SOME APPLICATIONS OF POLARITY THEORYIN GEOMETRIC INEQUALITIES

应用极性理论研究单形的度量性质 ,获得单形的一组替换定理 .利用这组替换定理可从单形的某些类型的等式或不等式出发 ,通过几何不变量的替换 ,获得单形的一些新的等式或不等式 ,作为其应用 ,获得了与单形内任一点有关的一组几何不等式以及关于单形 k维中面的一组几何不等式 .

This paper establishes a group of replacement theorems by using polarity theory of simplices. It can obtain some new equalities or inequalities from some equalities or inequalities by using these replacement theorems and replacing some geometric invariant. As its applications, it gets some geometric inequalities concerning any given point in a simplex and k dimensional middle sections of the simplex.