平面凸曲线的保长度流与几何不等式
A Length-Preserving Flow for Planar Convex Curves and Geometric Inequalities
摘要: 本文主要研究一个平面凸曲线的保长度流及其应用。在该保长度流下，演化曲线保持凸性，且收敛到一个圆。作为该流的应用，得到曲率型不等式和反向等周不等式。
Abstract: This article mainly studies the length-preserving flow of convex curves and its applications. Under this length-preserving flow, the evolving curve is still convex, and converges to a circle. As applications of this flow, curvature-type inequality and reverse isoperimetric inequality can be obtained.
文章引用：朱洪玉, Xaytou Yanenglor. 平面凸曲线的保长度流与几何不等式[J]. 理论数学, 2024, 14(5): 115-121. https://doi.org/10.12677/pm.2024.145167

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