The Stability of Veljan-Korchmaros's Inequality
Tongyi Ma · Chinese Annals of Mathematics · 2008
It is very difficult to find the formula of support function or radial function of simplices in Euclidean space E~n(n≥2),therefore the deviation metric of two simplices is difficult to realize by Hausdorff metric or radial metric.The study of stability of geometric inequalities of simplices is also difficult.In this paper,the problem of the deviation regular metric is solved by introducing the definition of the deviation regular metric of two sim- plices.The definition based on the fact that edge lengthes of simplex plays an important affect when someone define the simplex.Moreover,stability version of well-known Veljan- Korchmaros inequality is established.As application,some stability versions of a series of Veljan-Korchmaros models inequalities are established.