On The Bonnesen-type Inequalities For The Tetrahedral

This paper mainly research isopermetric deficit estimation of tetrahedron and Bonnesen-type Aleksandrov-Fenchel inequalities for symmetric convex body about the origin.Our first area of work mainly involves deficit estimation of tetrahedron in three dimensional Euclidean space.Because of the complexity of tetrahedral structure,it is difficult to discuss its isopermetric deficit estimation by including measure idea,so there is little research result on tetrahedron and even the other polyhedron so far.We use the relations of the surface area,volume,radius of inscribed sphere and radius of circumscribed sphere of tetrahedron,and following a series of geometric inequalities and the average value inequalities,we derive some Bonnesen-type inequalities of tetrahedron.Furthermore we give some new inverse Bonnesen-type inequalities of tetrahedron.The results of the study surface,with tetrahedron as an example can be discussed isopermetric deficit of other polyhedron.The second major area of work involves Bonnesen-type Aleksandrov-Fenchel inequalities for symmetric convex body about the origin.We use Aleksandrov-Fenchel inequalities,earning Bonnesen-type Aleksandrov-Fenchel inequalities for symmetric convex body about the origin,furthermore we give some lower bound of Aleksandrov-Fenchel isopermetric genus of symmetric convex body about the origin.Particular,we get partial results in two dimensional Euclidean plane three dimensional Euclidean space.The results of the study appear to this content and Log-Minkowski problem for research the uniqueness problem of convex body uniform pyramidal product measure.