一种新度量下Veljan-Korchmaros型不等式的稳定性

Stability of Veljan-Korchmaros Type Inequalities on a New Metric

本文利用n维单形与其共超球的n维正则单形的偏差,引进了单行"R-偏差"度量的概念,从而证明了单行的Veljan-Korchmaros不等式,以及中面型和中线型Veljan-Korchmaros型不等式是稳定的,并给出这些几何不等式的稳定性版本。

In this paper, the problem of the deviation regular metric is solved by introducing the definition of the R-deviation regular metric of an -simplex and an -dimensional regular simplex, which are in a sphere. The definition based on the fact that edge length of simplex plays an important role when defining the simplex. We prove that Veljian-Korchmaros type inequalities are all stable, and give the stability versions of these geometric inequalities for a simplex.