%A Xu Dong,Yan Zhang,Chunna Zeng,Xingxing Wang %T The General Inverse Bonnesen-Style Inequalities in $\mathbb{R}^n$ %0 Journal Article %D 2022 %J Acta mathematica scientia,Series A %R %P 641-650 %V 42 %N 3 %U {http://121.43.60.238/sxwlxbA/CN/abstract/article_16687.shtml} %8 2022-06-26 %X

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 Bonnesen-type inequalities in the plane. Finally, the best estimate between the results of three upper bounds is given.