平面Bonnesen型不等式

doi:10.12386/A2007sxxb0163

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数学学报 ›› 2007, Vol. 50 ›› Issue (6) : 1397-140. DOI: 10.12386/A2007sxxb0163

论文

平面Bonnesen型不等式

周家足;

作者信息 +

On Bonnesen-Type Inequalities

Jia Zu ZHOU

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文章历史 +

摘要

将用积分几何方法给出平面等周不等式以及Bonnesen型不等式,平面区域D的面积、周长、最大内接园半径及最小外接园半径的一些几何不等式的简单证明.

Abstract

We will derive the plane isoperimetric inequality and the Bonnesen's isoperi- metric inequality by the method of integral geometry.We give simplified proofs of some geometric inequalities about the area,the length,the in-radius and the out-radius of a plane domain D.