Regularity of inverse mean curvature flow in asymptotically hyperbolic manifolds with dimension $3$

Yuguang Shi, Jintian Zhu

Published 2018-11-15Version 1

By making use of nice behavior of Hawking mass of slices of weak solution of the inverse mean curvature flow in three dimensional asymptotically hyperbolic manifolds, we are able to show that each slice of flow is star-shaped after a long time, and then we get the regularity of the weak solution of the inverse mean curvature flow in asymptotically ADS-Schwarzschild manifolds with total mass $m> 0$.