A Note on the Reverse Isoperimetric Inequality

被引：13
|
作者：
Gao, Xiang [1 ]
机构：
[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
来源：
RESULTS IN MATHEMATICS | 2011年 / 59卷 / 1-2期
关键词：
Fourier series; Isoperimetric inequality; stability;
D O I：
10.1007/s00025-010-0056-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we derive an improved sharp version of a reverse isoperimetric inequality for convex planar curves of Pan and Zhang (Beitrage Algebra Geom 48:303-308, 2007), with a simpler Fourier series proof. Moreover our result also confirm a conjecture by Pan et al. (J Math Inequal (preprint), 2010). Furthermore we also present a stability property of our reverse isoperimetric inequality (near equality implies curve nearly circular).
引用
收藏
页码：83 / 90
页数：8
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