The inverse mean curvature flow in rotationally symmetric spaces

Abstract

In this paper, the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally symmetric spaces is studied. It is proved that the flow converges to a unique geodesic sphere, i.e., every principle curvature of the hypersurfaces converges to a same constant under the flow.

Keywords

Asymptotic behavior / Inverse mean curvature flow / Hyperbolic space

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