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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曲率积分不变,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,极限状态下会收敛到一个有限圆.作为这个流的应用,我们将证明三个不等式,其中第二个不等式推广了逆等周不等式. |
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:云南师范大学2024年年度研究生科研创新基金~(YJSJJ23-B68),国家自然科学基金项目(面上项目,重点项目,重大项目) |
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Non-local curve flow in the plane and its application |
Liu zhishuai,杨紫秋,郭顺滋
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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 curvature integral invariant during evolution if and when the initial curve is a closed convex curve.We will prove the existence of this flow as a whole and that the evolution curve is non-increasing in perimeter and area and converges to a finite circle in the limit.
As an application of this flow, we will prove three inequalities, the second of which generalises the inverse isoperimetric inequality. |
Key words: closed convex curve flow existence convengence curvature |