Just as in surface diffusion, facets with zero weighted mean curvature
may be eliminated by having one neighbor overtake another. If a facet
with non-zero weighted mean curvature shrinks to zero length, then all
segments on its connected component must also be shrinking to zero
length. (As 
, 
, and unless the average 
also becomes infinite,
will be so as to lengthen rather than shrink the facet.)
This cannot happen if the
average is made separately for each connected component of
the surface (the case of a thin vapor layer), so in this case a facet
with 
nonzero will never shrink to zero length. But for
coarsening, where there is instantaneous long-range diffusion through
the vapor, it can certainly happen that small grains shrink while
larger ones grow.