Wave-type threshold dynamics and the hyperbolic mean curvature flow

Abstract

We introduce a method for computing interfacial motions governed by curvature dependent acceleration. Our method is a thresholding algorithm of the BMO-type which, instead of utilizing a diffusion process, thresholds evolution by the wave equation to obtain the desired interfacial dynamics. We also develop the numerical method and present results of its application, including an investigation of the volume preserving and multiphase motions.