Diffusion generated motion of curves on surfaces

We present a new method for computing the curvature-driven motion of a curve constrained to move on a given surface. It is based on the Diffusion Generated Motion algorithm, and retains both the novel simplicity of that method, as well as the natural extension to curves with junctions, to general geometric motion laws, and to higher dimensions. The result is an extremely simple algorithm for curvature-dependent motion on surfaces, wherein the only evolution operation is linear diffusion in three-dimensional Euclidean space.