关于垂足单形体积不等式的推广

关于n维单形的几何不等式研究,近期建立了许多重要几何不等式,然而,关于垂足单形几何不等式研究还是比较少。该文应用解析方法和几何不等式理论研究了n维欧氏空间En中n维单形与其内点的垂足单形之间的几何不等式问题,建立了n维单形与其垂足单形的体积的两类关系式;作为其特例,改进了关于垂足单形体积的几何不等式;在对主要结果的证明中,还获得了有关n维单形顶点角与二面角之间的一类不等式。

Generalization of inequalities for volumes of pedal simplexes

Recent studies on the geometric inequality for the n-dimensional simplex produce many important geometric inequalities;however,the study on the problem of the geometric inequality for the pedal simplex has been very few.In this paper,by using the analytic method and the theory of the geometric inequality,the problem of the geometric inequality for the pedal simplex of a simplex in En is discussed,and some inequalities for the volumes of a simplex and its pedal simplex are established.As the special case,some known inequalities for the volumes of the simplex and its pedal simplex are improved.At the same time,a class of inequalities for the vertex angle and the dihedral angle of the n-dimensional simplex are got in the proving of main results.