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This work considers the question of whether mean-curvature flow can bemodified to avoid the formation of singularities. We analyze thefinite-elements discretization and demonstrate why the original flow can resultin numerical instability due to division by zero. We propose a variation on theflow that removes the numerical instability in the discretization and show thatthis modification results in a simpler formulation for both the discretized andcontinuous formulations. We discuss the properties of the modified flow andpresent empirical evidence that not only does it define a stable surfaceevolution for genus-zero surfaces, but that the evolution converges to aconformal parameterization of the surface onto the sphere.

Can Mean-Curvature Flow Be Made Non-Singular?