平面闭曲线的Bonnesen型不等式

Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1601-1610.

The Bonnesen-type Inequalities for Plane Closed Curves

Rui Bin¹(),Xingxing Wang²(),Chunna Zeng^1,*()

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:2022-01-29 Online:2022-12-26 Published:2022-12-16
Contact: Chunna Zeng E-mail:3164873638@qq.com;m13098792429@163.com;zengchn@163.com
Supported by:
the Major Project of NSFC(12141101);the Young Top-Talent Program of Chongqing(CQYC2021059145);the NSF of Chongqing(cstc2020jcyj-msxmX0609);the NSF of Chongqing(cstc2019jcyj-msxmX0390);the Venture Innovation Support Program for Chongqing Overseas Returnees(cx2019155);the Technology Research Foundation of Chongqing Educational Committee(KJQN201900530);the Technology Research Foundation of Chongqing Educational Committee(KJZD-K202200509);the Graduate Scientific Research Innovation Project of Chongqing(CYS22556);the Graduate Scientific Research Innovation Project of Chongqing Normal University(YKC21036)

Abstract

Abstract:

The isoperimetric inequality is one of the most classical geometric inequalities in differential geometry. The stability of isoperimetric genus can be characterized by Bonnesentype inequality and Bottema-type inequality. In this paper, via the method of differential geometry, Wirtinger inequality, Sachs inequality and divergence theorem and so on, we investigate the Bonnesen-type inequalities and Bottema-type inequalities for plane closed curves, and obtain a series of new Bonnesen-type inequalities and Bottema-type inequalities for curvature integration.

Key words: Wirtinger inequality, Sachs inequality, Bonnesen-type inequality, Bottema-type inequality

CLC Number:

O186.5

Rui Bin,Xingxing Wang,Chunna Zeng. The Bonnesen-type Inequalities for Plane Closed Curves[J].Acta mathematica scientia,Series A, 2022, 42(6): 1601-1610.

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The Bonnesen-type Inequalities for Plane Closed Curves

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