R^(3)中四面体的几个新Bonnesen型不等式

Some New Bonnesen-Type Inequalities of the Tetrahedron in R^(3)

离散的等周问题在积分几何与凸几何中扮演着重要角色.等周亏格的稳定性可以由Bonnesen型不等式和逆Bonnesen型不等式来刻画.该文主要研究R^(3)中四面体的Bonnesen型不等式和逆Bonnesen型不等式,获得了四面体的几个新的Bonnesen型不等式,并提供了不同于Sturm[15]关于四面体的等周不等式的一种简化证明;最后获得了几个用四面体内切球半径以及外接球半径表示的逆Bonnesen型不等式.

Discrete isoperimetric problems play an important role in integral geometry and convex geometry.The stability of isoperimetric deficit can be characterized by Bonnesen-type inequality and inverse Bonnesen-type inequality.In this paper,we study the Bonnesen-type inequality and the inverse Bonnesen-type inequality for Tetrahedra in R3.And we obtain several new Bonnesen-type inequalities for Tetrahedra.It provides a simplified proof which is different from the isoperimetric inequality for Tetrahedra in Sturm[15];finally,four inverse Bonnesen-type inequalities in terms of the radius of the circumscribed sphere and the radius of the circumscribed sphere are obtained.