A Gradient Flow for Menger Curvature

We consider an approach for a gradient flow according to Menger curvature for knots in 3-dimensional space. Menger curvature is a triple intergal over the inverse of the circumradius given by three points on a closed curve to a fixed power, where the circumradius is the radius of the corresponding circumcircle. After an overview of properties of this energy and its
discretization we present a collection of example illustrations, showing numerical simulations of the flow. In the end we discuss possible further directions of research.