$\mathbb{R}^n$中的广义逆Bonnesen型不等式

Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 641-650.

The General Inverse Bonnesen-Style Inequalities in $\mathbb{R}^n$

Xu Dong¹(),Yan Zhang¹(),Chunna Zeng^1,*(),Xingxing Wang²()

¹ School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
² School of Mathematics and Statistics, Shanghai Lixin University of Accounting and Finance, Shanghai 201620

Received:2021-08-04 Online:2022-06-26 Published:2022-05-09
Contact: Chunna Zeng E-mail:2931574183@qq.com;zengchn@163.com;2279282928@qq.com;m13098792429@163.com
Supported by:
the NSFC(11801048);the Young Top-Talent Program of Chongqing(CQYC2021059145);the NSF of Chongqing(cstc2020jcyj-msxmX0609);the Venture Innovation Support Program for Chongqing Overseas Returnees(cx2018034);the Venture Innovation Support Program for Chongqing Overseas Returnees(cx2019155);the Technology Research Foundation of Chongqing Educational Committee(KJQN201900530)

Abstract

Abstract:

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.

Key words: Aleksandrov-fenchel inequalities, Inverse Bonnesen type inequality, Quermassintegrals

CLC Number:

O186.5

Xu Dong,Yan Zhang,Chunna Zeng,Xingxing Wang. The General Inverse Bonnesen-Style Inequalities in $\mathbb{R}^n$[J].Acta mathematica scientia,Series A, 2022, 42(3): 641-650.

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The General Inverse Bonnesen-Style Inequalities in $\mathbb{R}^n$

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