Sipos A. András (BME, Department of Morphology and Geometric Modeling): On curves evolving under curvature-driven flows

Abstract:

The evolution of non-intersecting, smooth, closed curves under curvature-driven flows is investigated. Assuming sole generic saddle-node bifurcations, we show that the number of critical points of the curvature function κ is non-increasing. As the number of critical points of the curvature is closely related to the vertices of the evolute, the flow associated with the evolution of the evolute is derived. Finally, results about the evolution of the support function are collected and applied to explain unexpected shapes in nature.

The presented results are based on joint work with Gábor Domokos.