Abstract:

Using the theory and method of distance geometry,  the problems of stability of some geometric inequalities for an n-dimensional simplex in the Euclidean space is studied. From the deviation regular metric of two simplexes, the stabilities of four important geometric inequalities of an n-dimensional simplex are proved, and the stability versions of these geometric inequalities for a simplex are given.

Key words:  simplex; circum-radius; in-radius; radius of escribed ball; stability