Volume preserving mean curvature flow in the Hyperbolic space

Details Volume preserving mean curvature flow in the Hyperbolic space Volume preserving mean curvature flow in the Hyperbolic space

2006-11-08

arxiv.org/abs/math/0611216v1

Mathematics

Differential Geometry

Scientific paper

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.

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