Research On Geometric Inequalities Of Simplexes In Eudcliden Space

Using theory and method of distance geometry to study the voluems of two simplexes, and using the deviation regular metric to studythe circumradii of simplexes inequality and the stability of two inequalities for tangent points simplex, the stability versions of that are given. The thesis contains five chapters, as follows:In section one, the main content is simple introduction about development geometric inequalities, especially its development in china in last20years. And introduce some inequalities.In section two, introduces two n-dimensional simplexes Neuberg-Pedoe inequality, the volumes of two n-dimensional simplexes and their k-subsimplexes in the Euclidean space En.Two related inequalities are established and some known inequalities are improvedIn section three, using analytic method and theory of geometric inequality, conjeture an Euler inequality in thesimplex. A geometric inequality for the circumradius and distance of interior point to side faces is established, which far improves Euler inequalityIn section four, The stability of two inequalities forthe circumradii of simplexes are proved, and th e stability versions of these inequalities are given.At last, Using the deviation regular metric of a simplex and theory of geometric inequalities to prove the stability of two inequalities for tangent points simplex, also the stability versions of these inequalities are given.