  By making use of the nice behavior of Hawking masses of slices of a weak
solution of inverse mean curvature flow in three dimensional asymptotically
hyperbolic manifolds, we are able to show that each slice of the flow is
star-shaped after a long time, and then we get the regularity of the weak
solution of inverse mean curvature flow in asymptotically hyperbolic manifolds.
As an application, we prove that the limit of Hawking mass of the slices of a
weak solution of inverse mean curvature flow with any connected $C^2$-smooth
surface as initial data in asymptotically ADS-Schwarzschild manifolds with
positive mass is bigger than or equal to the total mass, which is completely
different from the situation in asymptotically flat case.
