R^(n)中的广义逆Bonnesen型不等式

The General Inverse Bonnesen-Style Inequalities in R^(n)

等周问题在积分几何中具有举足轻重的地位.该文主要研究R^(n)中等周不等式的逆形式,即广义逆Bonnesen型不等式.该文获得了R^(n)中几个新广义等周亏格上界的结果,作为推论,得到了更一般的平面上的逆Bonnesen型不等式;最后给出其中三个上界结果之间的最佳估计.

The isoperimetric problem plays an important role in integral geometry.In this paper we mainly investigate the inverse form of the isoperimetric inequality,i.e.the general inverse Bonnesen-type inequalities.The upper bounds of several new general isoperimetric genus are obtained.Futhermore,as corollaries,we get a series of classical inverse Bonnesentype inequalities in the plane.Finally,the best estimate between the results of three upper bounds is given.