Mean curvature flow of higher codimension in Riemannian manifolds
Mean curvature flow of higher codimension in Riemannian manifolds
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发表时间：
2012-03
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通讯作者：
Kefeng Liu;Hong-wei Xu;Entao Zhao
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作者：
Kefeng Liu;Hong-wei Xu;Entao Zhao
我们研究了有界几何黎曼流形中任意余维平均曲率流的收敛性。我们证明，如果初始子流形满足收缩条件，则沿着平均曲率流动，子流形在有限时间内平滑收缩到圆点。因此，我们得到了黎曼流形中子流形的可微球定理。
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching condition, then along the mean curvature flow the submanifold contracts smoothly to a round point in finite time. As a consequence we obtain a differentiable sphere theorem for submanifolds in a Riemannian manifold.