平面闭曲线的Bonnesen型不等式  

The Bonnesen-type Inequalities for Plane Closed Curves

作　　者：宾芮 王星星 曾春娜 Bin Rui;Wang Xingxing;Zeng Chunna(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331;School of Mathematics and Statistics,Shanghai Lixin University of Accounting and Finance,Shanghai 201620)

机构地区：[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

出　　处：《数学物理学报（A辑）》2022年第6期1601-1609,共9页Acta Mathematica Scientia

基　　金：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,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,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)。

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.The isoperimetric inequality is one of the most classical geometric inequalities in differential geometry.The stability of isoperimetric genus can be characterized by Bonnesen-type 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.

关 键 词：WIRTINGER不等式 Sachs不等式 BONNESEN型不等式 Bottema型不等式 

分 类 号：O186.5[理学—数学]