Inverse mean curvature flows in warped product manifolds

We study inverse mean curvature flows of starshaped, mean convex hypersurfaces in warped product manifolds with a positive warping factor $\phi (r)$. If ${\phi }^{\mathrm{\prime }}(r)>0$ and ${\phi }^{\mathrm{\prime }\mathrm{\prime }}(r)\ge 0$, we show that these flows exist for all times, remain starshaped and mean convex. Plus the positivity of ${\phi }^{\mathrm{\prime }\mathrm{\prime }}(r)$ and a curvature condition we obtain a lower positive bound of mean curvature along these flows independent of the initial mean curvature. We also give a sufficient condition to extend the asymptotic behavior of these flows in Euclidean spaces into some more general warped product manifolds.