平面上面积长度具有单调性的闭凸曲线流及其应用

Closed-convex Curve Flow with Monotonicity of Area Length on the Plane

研究了速度和函数中含有支撑函数的闭凸曲线非局部流,在非局部项可微函数的不同取值情况下,给出了演化曲线面积和长度对应的单调性,得到了演化曲线保持闭凸性,光滑闭凸曲线在该流下存在唯一解且最终收敛于一个圆.特别地,通过该曲线收缩流给出了平面上Ros定理的加强形式.

In this paper,the non-local flow of the closed convex curve with support function in the velocity function is studied,and the monotonicity corresponding to the area length of the evolution curve is given under the different values of the non-local term differentiable function,and the evolution curve maintains the closed convexity,and the smooth closed convex curve has a unique solution under the flow and finally converges to a circle.In particular,the contraction flow through this curve gives a strengthened form of Ros′s theorem on the plane.