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
相关论文
共 50 条
  • [11] A NEW REVERSE ISOPERIMETRIC INEQUALITY AND ITS STABILITY
    Gao, Xiang
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2012, 15 (03): : 733 - 743
  • [12] A reverse isoperimetric inequality for planar (α, β)-convex bodies
    Croce, Gisella
    Fattah, Zakaria
    Pisante, Giovanni
    ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2022, 28
  • [13] Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle
    Krejcirik, David
    Lotoreichik, Vladimir
    Vu, Tuyen
    APPLIED MATHEMATICS AND OPTIMIZATION, 2023, 88 (02):
  • [14] A reverse isoperimetric inequality for J-holomorphic curves
    Groman, Yoel
    Solomon, Jake P.
    GEOMETRIC AND FUNCTIONAL ANALYSIS, 2014, 24 (05) : 1448 - 1515
  • [15] A reverse isoperimetric inequality for J-holomorphic curves
    Yoel Groman
    Jake P. Solomon
    Geometric and Functional Analysis, 2014, 24 : 1448 - 1515
  • [16] A reverse isoperimetric inequality for embedded starshaped plane curves
    Jianbo Fang
    Archiv der Mathematik, 2017, 108 : 621 - 624
  • [17] Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle
    David Krejčiřík
    Vladimir Lotoreichik
    Tuyen Vu
    Applied Mathematics & Optimization, 2023, 88
  • [18] A reverse isoperimetric inequality for embedded starshaped plane curves
    Fang, Jianbo
    ARCHIV DER MATHEMATIK, 2017, 108 (06) : 621 - 624
  • [19] A reverse isoperimetric inequality for convex shapes with inclusion constraint
    Bogosel, Beniamin
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 540 (02)
  • [20] ISOTROPIC MEASURES AND STRONGER FORMS OF THE REVERSE ISOPERIMETRIC INEQUALITY
    Boroczky, Karoly J.
    Hug, Daniel
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (10) : 6987 - 7019
12345