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| 摘要: |
| 本文研究了平面上$C^2$闭凸曲线的极坐标形式$\{O;\rho(\theta)\}$，运用Bonnesen不等式的推广形式$^{[1,2]}$，得到关于$\rho$及$\rho_\theta$的一些积分形式的Bonnesen 型不等式，使得我们很容易得到等周不等式取等时的条件。 |
| 关键词: 等周不等式 闭凸曲线 极坐标 Bonnesen不等式 |
| DOI： |
| 分类号:O186.5 ， O 186.11 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| Several Bonnesen-style Inequalities about Polar Coordinates |
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ZHENG Gao-Feng,ZHOU Yang
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| Abstract: |
| In this paper, we study $C^2$ convex closed plane curve inpolar coordinates $\{O;\rho(\theta)\}$. By using the extended Bonnesen inequalities$^{[1,2]}$, we obtain some new Bonnesen-type inequalities about integration of $\rho$ and $\rho_\theta$,so that wecan easily get the conditions under which equality in the isoperimetric inequality holds. |
| Key words: Isoperimetric Inequality Convex Closed Curve Polar Coordinates Bonnesen Inequality |
