数学杂志2025，Vol.45Issue(5)：409-416,8.
平面上非局部曲线流及其应用
NON-LOCAL CURVE FLOW IN THE PLANE AND ITS APPLICATION
摘要
Abstract
In this paper,we study a family of non-local curve flows in the Euclidean plane,which remain convex and ∫2π0 kdθ 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 this flow,we will prove three inequalities,with the second inequality extending the inverse isoperimetric inequality.关键词
闭凸曲线流/存在性/收敛性/曲率Key words
closed convex curve flow/existence/Convengence/curvature分类
数理科学引用本文复制引用
刘志帅,杨紫秋,郭顺滋..平面上非局部曲线流及其应用[J].数学杂志,2025,45(5):409-416,8.基金项目
国家自然科学基金项目资助(12261105) （12261105）
云南省教育厅科学研究基金项目资助(2024Y154) （2024Y154）
云南师范大学2024年年度研究生科研创新基金资助(YJSJJ23-B68). （YJSJJ23-B68）
