关于单形几个几何不等式的稳定性

摘要

Using the theory and methods of metric geometry to study the problems of stability, which is some geometric inequalities for an n-simplex in the n-dimensional Euclidean space E". From the deviation regular metric of two simplexes, we prove that Sallee-Alexander's and Yang-Zhang's inequalities for the width of an n-simplex are all stable, and also prove that Veljan-Korchmaros's inequalities for the medians and the middle sections of an n-simplex are all stable. The stability versions of these geometric inequalities for a simplex are established,and these geometric inequalities are improved.%利用度量几何的理论与方法研究了n维欧氏空间En中n维单形几个几何不等式的稳定性,从2个单形偏正度量证明了n维单形宽度的Sallee-Alexander不等式与杨-张不等式是稳定的；证明了n维单形中线型与中面型Veljan-Korchmaros不等式是稳定的.并给出了单形的几何不等式的稳定性版本,从而推广了这类几何不等式.