The Hyperbolic Length-Preserving Curvature Difference Flow of Plane Curves

In this paper, we study the curvature difference flow about two smooth strictly convex closed plane curves. The two initial curves have the same length, one of them is fixed and another is evolving. We show that, the flow is length-preserving and exists for a short time [0, T]. From the analysis of the solutions to the flow, we can't get any information about keeping convexity and explosion.