In this section we reexamine in the crystalline formulation two limiting cases of geometric interface motion that conserve volume. The first arises from surface diffusion (SD); with isotropic surfaces, this is motion by the Laplacian of mean curvature. The second arises from surface attachment limited kinetics (SALK) with fast transport through a surrounding surface layer or medium assumed; with isotropic surfaces and linear kinetics, this is motion by mean curvature modified for volume conservation to become motion by the difference between curvature and a suitably weighted average of mean curvature.
with a volume
constraint