简单闭凸曲线曲率积分不等式的递推关系
Recurrence Relation of Curvature Integral Inequalities for Simple Closed Convex Curves
摘要: 本文主要研究平面上简单闭凸曲线的曲率积分不等式。利用单位速率外法向流对Green-Osher的结果进行了简化证明，发现了曲率积分不等式高阶和低阶情况的一个递推关系，对以前的结果进行了推广，并且发现了一个特殊的函数。
Abstract: In this paper, we mainly study the curvature integral inequality of simple closed convex curves on the plane. We use the unit-speed outward normal flow to simplify the proof of Green-Osher's results, find a recurrence relationship between the high-order and low-order cases of the curvature integral inequality, generalize the previous results, and find a special function.
文章引用：李亚尊, 张永志. 简单闭凸曲线曲率积分不等式的递推关系[J]. 理论数学, 2023, 13(3): 375-380. https://doi.org/10.12677/PM.2023.133041

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