| 1. | Under this flow , the convex initial curve will preserve its perimeter , enlarge the enclosed area and make its curvature to be positive definitely . and as the time lasts , it will become more and more circular , and finally , as the time goes to infinity , the curve will converge to a circle in the hausdorff metric
本文证明在这种新的曲线流之下，闭凸曲线周长保持不变、所围区域的面积不断增大而曲率保持恒正(从而保持凸性) ，并且，随着时间的推移曲线变得越来越圆，最终当时间t趋向于无穷大时，曲线在hausdorff度量意义下收敛到一个圆周。 |
