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In this paper we study Inverse Mean Curvature Flow (IMCF) on manifolds thatare conformal to a warped product manifold. To this end, we show how thegradient conformal vector field in warped product manifolds is related to theconformal vector field on the conformal metric and use this to gain control ofthe flow in order to show long time existence. Connections are made to recentresults of the author on stability of the positive mass theorem (PMT) and theRiemannian Penrose inequality (RPI) where long time existence of IMCF is animportant assumption.

Long Time Existence of IMCF on Metrics Conformal to Warped Product Manifolds