平面闭凸曲线的一类新的熵不变流及其应用

A new Class of Entropy Invariant Flows for Planar Closed Convex Curves and Its Applications

研究了平面上保持闭凸曲线熵不变的一类新的曲线流,证明了若初始曲线是闭凸的,则演化曲线保持闭凸,且它的面积和长度随时间都不断减小,但是曲线的熵能量在演化过程中为常数,当时间趋于无穷时,它的最终收敛形状是一个圆.同时应用该流证明了平面曲线的熵不等式.

In this paper,we study a new class of curved flows that keep the entropy of a closed convex curve unchanged on a plane,and prove that if the initial curve is closed convex,the evolution curve remains closed convex,and its area and length decrease with time,but the entropy energy of the curve is constant in the evolution process,and when the time goes to infinity,its final convergence shape is a circle.At the same time,the entropy inequality of plane curve is proved by using this flow.