一类凸曲线流在Ros等周不等式中的应用
The Application of a Kind of Convex Curve Flows to Rose Isoperimetric Inequalities
摘要: 通过平面中一类面积非减的凸曲线流，曲线在发展过程中保持凸性不变，具有全局存在性，且当时间趋于无穷大时，曲线在C0范数下收敛到圆。我们建立该曲线流的单调公式，给出了平面上Ros等周不等式新的证明。
Abstract: By convex curve flow with non-decreasing area in the plane, the curve remains convex and exists globally, and the evolving curve converges to a circle as the time goes to infinity. A new proof of the plane Rose isoperimetric inequalities is given by establishing the monotone formulas along the curve flow.
文章引用：陈晓. 一类凸曲线流在Ros等周不等式中的应用[J]. 理论数学, 2025, 15(3): 56-62. https://doi.org/10.12677/pm.2025.153076

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