IUMJ

Title: Volume preserving mean curvature flow in the hyperbolic space

Authors: Esther Cabezas-Rivas and Vicente Miquel

Issue: Volume 56 (2007), Issue 5, 2061-2086

Abstract:

We prove: "If $M$ is a compact hypersurface of the hyperbolic space, convex by horospheres and evolving by the volume preserving mean curvature flow, then it flows for all time, convexity by horospheres is preserved and the flow converges, exponentially, to a geodesic sphere". In addition, we show that the same conclusions about long time existence and convergence hold if $M$ is not convex by horospheres but it is close enough to a geodesic sphere.