Can Mean-Curvature Flow be Modified to be Non-singular?

This work considers the question of whether mean‐curvature flow can be modified to avoid the formation of singularities. We analyze the finite‐elements discretization and demonstrate why the original flow can result in numerical instability due to division by zero. We propose a variation on the flow that removes the numerical instability in the discretization and show that this modification results in a simpler expression for both the discretized and continuous formulations. We discuss the properties of the modified flow and present empirical evidence that not only does it define a stable surface evolution for genus‐zero surfaces, but that the evolution converges to a conformal parameterization of the surface onto the sphere.