摘要
关于Euclidean空间E^n(n≥2)中单形的几何不等式,由于支撑函数或径向函数的表达式很难找到,因此一般很难用Hausdorff度量或径向度量来度量两个单形的"偏差",使得涉及单形的几何不等式的稳定性的研究比较困难.利用单形棱长在确定单形时起决定性作用这一事实,引进了两个单形"偏正"度量的概念,从而较好地解决了单形偏正度量的问题,并建立了著名的Veljan-Korchmaros不等式的稳定性版本.作为推论,还导出了一系列Veljan-Korchmaros型不等式的稳定性版本.
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.
出处
《数学年刊（A辑）》
CSCD
北大核心
2008年第3期399-412,共14页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10671117)
甘肃省教育厅科研基金(No.0709-03)资助的项目
