Harnack estimate for the mean curvature flow
Harnack estimate for the mean curvature flow
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DOI：
10.4310/jdg/1214456010
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发表时间：
1995
影响因子：
2.5
通讯作者：
R. Hamilton
中科院分区：
文献类型：
--
作者：
R. Hamilton
1.结果我们考虑欧氏空间R中超曲面M的平均曲率的演化。这是由Huisken首先研究的[3]。在这个流动中，M上的每个点Y以等于平均曲率H的速度沿单位法向量N的方向移动，第二基本形式H（V，V）在切向量V上的迹。我们将注意力限制在光滑且紧凑的解上，否则就完成了有界的第二基本形式。1.1.主要定理A.对于t > 0的平均曲率流的任何弱凸解，我们有
1. The result We consider the evolution of a hypersurface M in Euclidean space R by its mean curvature. This was first studied by Huisken [3]. In this flow each point Y on M moves in the direction of the unit normal vector N with velocity equal to the mean curvature H, the trace of the second fundamental form H(V, V) over the tangent vectors V. We confine our attention to solutions which are smooth and either compact, or else are complete with bounded second fundamental form. 1.1. Main Theorem A. For any weakly convex solution to the mean curvature flow for t > 0 we have