The Stability Of Some Geometric Inequalities For N-dimensional Simplex

This master dissertation researches the geometric inequalities of simplex,focused re-searches on the stability of geometric inequalities. In this paper, by using the deviation regular and the theory of geometric inequality, We research and prove that some geomet-ric inequalities are all stable.and give the stability versions of these geometric inequalities. The thesis contains four chapters, as follows:Chapter1The main content is simple introduction about development geometric inequalities, especially its development in china in last20years.And then,we introduce some detail about the stability of geometric inequalities and give some concept.At last,we introduce this thesis’s main aspects and some results we gain.Chapter2The main content is the introduction about a basic concept concerning the width of simplex.And then,we prove that Sallee-Alexander’s inequality for the width of an n-simplex is stable,The stability version of Sallee-Alexander’s inequality for the width of an n-simplex is established,and the Sallee-Alexander inequality is materiality generalizedChapter3The main content is the introduction some basic concept about foot point simplex and tangent point simplex. And then,we prove that an inequality of foot point simplex and an inequality of tangent point simplex are all stable, and also prove that an generalize inequality of Euler and an inequality for the high of simplex are all stable. The stability versions of these geometric inequalities for a simplex are established,and these geometric inequalities are proved.Chapter4The main content is the introduction about researching on Veljan-Korchmaros inequality.And then, the stability versions of Veljan-Korchmaros inequality is established, and The stability versions of Veljan-Korchmaros is generalized.