Semi-Discrete Linear Hyperbolic Curvature flow

Abstract

We consider evolution of piecewise linear curves with boundary by linear hyperbolic curvature flows. Given appropriate boundary behaviours we find corresponding self-similar solutions. More generally, given any specific boundary trajectories we write down general solutions using finite Fourier expansions. Finally we consider the problem of evolving one piecewise linear curve to another using nonhomogeneous linear hyperbolic flow.

36 pages, 11 figures