On the inverse mean curvature flow in warped product manifolds

Abstract

We consider the warped product manifold, ${\mathbb{R}}_{+}{\times }_{\mathbf{Id}}{M}^n$, 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 what sufficient curvature condition is required of $\sigma$ to ensure that a solution to the inverse mean curvature flow - commencing with a star-shaped surface - exists for all times $t>0$.

This result was obtained in the author's Master's thesis, submitted in December 2014 to the FU Berlin

Cited by in corpus (1)

• Inverse curvature flows in Riemannian warped products