逆向等周型不等式的研究进展

Advances in Inverse Isoperimetric Inequalities

数学中最经典的几何不等式就是等周不等式,它刻画了欧式平面中的由简单闭曲线所围区域的面积与周长之间的关系。本文从最经典的等周不等式出发,探究逆向等周不等式的发展进程并归纳总结近年来逆向等周不等式的研究成果,主要从三个方面分别介绍了逆向等周不等式在平面卵形域、高维欧式曲面、流行曲面及一些特殊曲面的发展过程及主要研究成果。

The most classical geometric inequality in mathematics is the isoperimetric inequality,which de-scribes the relationship between the area and perimeter of the region enclosed by a simple close curve in a Euclidean plane.Starting from the most classical isoperimetric inequalities,this paper explores the development process of reverse isoperimetric inequalities and summarizes the research results of reverse isoperimetric inequalities in recent years.It mainly introduces the development process and main research results of reverse isoperimetric inequalities in plane oval domain,high-dimensional Euclidean surface,popular surface and some special surface from three aspects.