In this work we extend the ODE Maximum principle of Hamilton to non-compact hypersurfaces using the Omari-Yau maximum principle at infinity. As an application of this result, we investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over horospheres in $\mathbb{ H}^{ n+1}$ and show long time existence of the flow as well as asymptotic convergence to horospheres.
Categories: math.DG