Abstract
In this paper we introduce a new geometric flow with rotational invariance and prove that, under this kind of  flow, an arbitrary smooth closed contractible hypersurface in the Euclidean space Rn+1 (n ¸ 1) converges to Sn in the C1-topology as t goes to the infinity. This result covers the well-known theorem of Gage and Hamilton in [4] for the curvature flow of plane curves and the famous result of Huisken in [5] on the °ow by mean curvature of convex surfaces, respectively.

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