Inverse mean curvature flow evolves a hypersurface in its normal direction at speed equal to the reciprocal of the positive sum 
of its principal curvatures.
Here the sum is used rather than their average as in the mean
curvature convention. For an embedding 
with outward unit normal 
, its smooth equation is
 |
A level-set description uses 
away from critical points. Weak
solutions permit jumps across regions where the smooth evolution breaks down. Huisken
and Ilmanen (2001) used such weak solutions to prove the three-dimensional Riemannian
Penrose inequality for a connected outermost minimal
surface. For an expanding sphere in 
, its radius satisfies 
.
