Anisotropic-Length-Preserving Weighted Anisotropic Curvature Flows

In this paper, we study the anisotropic-length-preserving weighted anisotropic curvature flow for smooth convex closed plane curves. For any smooth, embedded, closed, convex initial curve, the flow exists smoothly for all time, and the anisotropic curvature converges smoothly to that of the boundary of the corresponding homothetic Wulff shape as time tends to infinity.