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We consider the warped product manifold, $\mathbb{R}_+ \times_{\bf{Id}} M^n$,with Riemannian metric $\gamma\equiv \mathrm{d} r^2 \oplus r^2 \sigma$, where$(M^n, \sigma)$ is a smooth closed Riemannian $n$-manifold. We investigate whatsufficient curvature condition is required of $\sigma$ to ensure that asolution to the inverse mean curvature flow - commencing with a star-shapedsurface - exists for all times $t>0$.

On the inverse mean curvature flow in warped product manifolds