Convexity phenomena arising in an area-preserving crystalline curvature flow (Q6617864)

The paper examines the behaviour of polygonal curves under area-preserving crystalline curvature flow. The authors demonstrate a ``convexity phenomenon'', wherein a solution polygon, starting from a non-convex initial polygon, becomes convex within a finite time. To establish this result, the authors provide a complete classification of edge-disappearance patterns and prove that all edges with zero curvature vanish in finite time. Furthermore, they show that the evolution of the flow can continue beyond these edge-disappearance singularities.\N\NFor the entire collection see [Zbl 1541.35006].