几类闭凸曲线的曲率积分不等式  

Curvature Integral Inequalitiesfor Some Classes of ClosedConvex Curves

作　　者：张泽源 赵会文 

机构地区：[1]云南师范大学数学学院,云南 昆明

出　　处：《理论数学》2023年第4期1056-1061,共6页Pure Mathematics

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。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 boundsdepend only on arc length and area.

关 键 词：凸函数 Green-Osher不等式 Steiner多项式 

分 类 号：O17[理学—数学]