平面闭曲线的Bonnesen型不等式

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1601-1610.

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平面闭曲线的Bonnesen型不等式

宾芮¹(),王星星²(),曾春娜^1,*()

¹ 重庆师范大学数学科学学院重庆 401331
² 上海立信会计金融学院统计与数学学院上海 201620

收稿日期:2022-01-29 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 曾春娜 E-mail:3164873638@qq.com;m13098792429@163.com;zengchn@163.com
作者简介:宾芮, E-mail: 3164873638@qq.com|王星星, E-mail: m13098792429@163.com
基金资助:
国家自然科学基金重大专项(12141101);重庆英才青年拔尖计划(CQYC2021059145);重庆市自然科学基金(cstc2020jcyj-msxmX0609);重庆市自然科学基金(cstc2019jcyj-msxmX0390);重庆市留学人员创新创业支持计划(cx2019155);重庆市教育委员会科学技术研究项目(KJQN201900530);重庆市教育委员会科学技术研究项目(KJZD-K202200509);重庆市研究生科研创新项目(CYS22556);重庆师范大学研究生科研创新项目(YKC21036)

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)

摘要/Abstract

摘要：

等周不等式是微分几何中最经典的几何不等式之一.等周亏格的稳定性可由Bonnesen型不等式和Bottema型不等式来刻画.该文主要利用微分几何的方法及Wirtinger不等式、Sachs不等式、散度定理等探索平面闭曲线的Bonnesen型不等式和Bottema型不等式, 获得了一系列新的Bonnesen型不等式及关于曲率积分的Bottema型不等式.

关键词: Wirtinger不等式, Sachs不等式, Bonnesen型不等式, Bottema型不等式

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

中图分类号:

O186.5

宾芮,王星星,曾春娜. 平面闭曲线的Bonnesen型不等式[J]. 数学物理学报, 2022, 42(6): 1601-1610.

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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平面闭曲线的Bonnesen型不等式

The Bonnesen-type Inequalities for Plane Closed Curves

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