几类闭凸曲线的曲率积分不等式
Curvature Integral Inequalitiesfor Some Classes of ClosedConvex Curves
DOI: 10.12677/PM.2023.134111, PDF, HTML,   
作者: 张泽源*, 赵会文：云南师范大学数学学院，云南 昆明
关键词: 凸函数；Green-Osher不等式；Steiner多项式；Convex Function； Green-Osher Inequality； Steiner Polynomial
摘要: Green-Osher不等式是一般严格凸函数的曲率积分不等式，本文则考虑一些常见的特殊凸函数在Green-Osher不等式中得到的曲率积分不等式，本文通过在Green-Osher不等式中，取平面闭凸曲线四类凸函数，得到了关于这些凸函数在曲率积分的精确下界，这些下界仅与弧长和面积有关。
Abstract: Green-Osher inequality is the integral of curvature for strictly convex functions in general, some special convex functions get curvature integral inequalities in Green-Osher inequality. In this paper, we apply four types of convex functions of plane closed convex curve to Green-Osher inequality. We get some exact lower bounds on the integration of these convex functions over the curvature. These lower bounds depend only on arc length and area.
文章引用：张泽源, 赵会文. 几类闭凸曲线的曲率积分不等式[J]. 理论数学, 2023, 13(4): 1056-1061. https://doi.org/10.12677/PM.2023.134111

参考文献

[1] Green, M. and Osher, S. (1999) Steiner Polynomials, Wulff Flows, and Some New Isoperimetric Inequalities for Convex Plane Curves. Asian Journal of Mathematics, 3, 659-676.
https://doi.org/10.4310/AJM.1999.v3.n3.a5
[2] 马磊, 曾春娜. 关于由率积分不等式的注记[J]. 数学杂志, 2014, 34(5): 925-930.
https://doi.org/10.13548/j.sxzz.2014.05.040
[3] 涂康. Wulff流情形下的一个积分不等式[J]. 广东石油化工学院学报, 2015, 25(1): 67-68+73.
[4] 王亚玲, 董旭, 曾春娜, 王星星. 凸由线的由率积分不等式[J/OL]. 数学学报(中文版): 1-10.
http://kns.cnki.net/kcms/detail/11.2038.o1.20221108.1653.008.html

为你推荐