由Γ-截面函数确定凸体

In this paper, we prove that any polygon P in R2 containing a fixed smooth. strictly convex and origin-symmetric body Γ whose boundary is real analytic in its interior, can be determined by its Γ-section functions among the polygons.     

凸体的包含测度(Ⅱ)

In this paper,several inequalities for inclusion measures of convex bodies were obtained.The inclusion measure was proved to have concavity by considering the property of relative inner parallel body.     

由Γ-截面函数确定凸体

In this paper, we prove that any polygon P in R2 containing a fixed smooth. strictly convex and origin-symmetric body Γ whose boundary is real analytic in its interior, can be determined by its Γ-section functions among the polygons.     

凸体的包含测度(II)

In this paper, several inequalities for inclusion measures of convex bodies were obtained. The inclusion measure was proved to have concavity by considering the property of relative inner parallel body.     

Firey linear combinations of convex bodies

For convex bodies, the Firey linear combinations were introduced and studied in several papers. In this paper the mean width of the Firey linear combinations of convex bodies is studied, and the lower bound of the mean width of the Firey linear combinations of convex body and its polar body is given.     

单形的径向平均体

In this paper, it is proved that the radial pth mean body RpK（p 〉 0） is homothetic to the difference body DK when K is a simplex, Furthermore, the equality Rp（Rq） = Rq（Rp） is established when p 〉 0 and q 〉 0. It is also proved the Brunn-Minkowski inequality of radial pth mean body of simplex and uniqueness property.     

关于单形的John定理

1 Introduction In 1948 , John proved that every convex body(i.e.,a compact ,convex subset with nonempty in-terior) inRncontains only one maxi mal(in volume)ellipsoid , which is known as the John ellipsoid . Whenthe John ellipsoid is the unit ballB2n,John has provedthe following theorem. Theorem1[1] LetCbe a convex body inRn. Theellipsoid of maxi mal volume inCisB2n,if and onlyifCcontainsB2nand there are some points (ui)1montheboundary ofCand positive numbers (ci)1mso that(a)∑mi=1ciui ui…     

凸体的包含测度(Ⅰ)

1 Introduction In [1] ,Zhang established certain geometric inequa-lities by considering the inclusion measure of a convexfigure containedin a convex body.Theyrelated thein-clusion measure to the mixed volumes of convex bo-dies ,and gave sharp lower and up…     

Inclusion measures of convex bodies （ Ⅰ ）

In this paper, the relations between inclusion measures of different bodies related to convex body K and the inclusion measure of convex body K itself were obtained.