Abstract
In this paper, the mean curvature type flow of star-shaped closed hypersurfaces in rotationally symmetric spaces is investigated. We prove that the flow exists for all times and converges exponentially to a sphere in the $C^{\infty}$ topology, enclosing the same volume as the initial hypersurfaces. This extends the corresponding result of space forms by Guan and Li (2015) to a large class of rotationally symmetric spaces.
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