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| 摘要: |
| 本文研究欧式平面上一族非局部曲线流,若当初始曲线是闭凸曲线,则在演化过程中它会保持凸性以及$\int_0^{2\pi} k^{\alpha-2}d\theta$不变,利用压缩映射原理,得到解的唯一性,本文将证明这个流的整体存在性,且演化曲线周长和面积非增,得到了演化曲线在极限状态下会收敛到一个圆.作为流的应用,将证明一个新的不等式. |
| 关键词: 闭凸曲线流 存在性 收敛性 曲率 |
| DOI： |
| 分类号:O186.1 |
| 基金项目: |
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| A Class of Planar Nonlocal Curve Flows and Their Applications |
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Liu zhishuai,郭
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| Abstract: |
| In this paper, we study a family of non-local curve flows in the Euclidean plane, which remain convex and $\int_0^{2\pi} k^{\alpha-2}d\theta$ invariant during evolution if and when the initial curve is a closed convex curve.Using the principle of compressed mapping, we obtain the uniqueness of the solution. In this paper, we will prove the global existence of this flow and that the length and area of the evolution curve are non-increasing. We will also show that the evolution curve converges to a finite circle in the limit state. As an application of the flow , we prove an inequality for convex plane curves. |
| Key words: closed convex curve flow existence convengence curvature. |
