| 摘要: |
| 本文研究了平面上C2闭凸曲线的极坐标形式{O；ρ（θ）}.运用Bonnesen不等式的推广形式[1，2]，得到关于ρ及ρθ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:O186.11 |
| 基金项目:国家自然科学基金资助（11171126；11571131）. |
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| SEVERAL BONNESEN-STYLE INEQUALITIES ABOUT POLAR COORDINATES |
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ZHENG Gao-feng, ZHOU Yang
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School of Mathematics and Statistics, China Central Normal University, Wuhan 430079, China
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| Abstract: |
| In this paper, we study C2 convex closed plane curve inpolar coordinates {O; ρ(θ)}. By using the extended Bonnesen inequalities [1, 2], we obtain some new Bonnesen-type inequalities about integration of ρ and ρθ, so that we can easily get the conditions under which equality in the isoperimetric inequality holds. |
| Key words: isoperimetric inequality convex closed curve polar coordinates Bonnesen inequality |
