论文标题
通用平均曲率流，具有圆柱奇异性I：正常形式和非平稳性
Generic mean curvature flows with cylindrical singularities I: the normal forms and nondegeneracy
论文作者
论文摘要
本文研究了平均曲率流的动力学，它接近圆柱奇异性。我们证明，在半径$ k \ sqrt {t} $的球中，可以将重新缩放的平均曲率流融合到平滑的广义圆柱体上，并在圆柱体上写成图形，而渐近学的正常形式。使用正常形式，我们可以定义圆柱奇异性的非平稳性，并且我们表明非排定圆柱形奇异性是在空间中分离出来的，具有平均凸面邻域，并且是I型。
This paper studies the dynamics of mean curvature flow as it approaches a cylindrical singularity. We proved that the rescaled mean curvature flow converging to a smooth generalized cylinder can be written as a graph over the cylinder in a ball of radius $K\sqrt{t}$, and a normal form of the asymptotics. Using the normal form, we can define the nondegeneracy of cylindrical singularities, and we show that nondegenerate cylindrical singularities are isolated in space, have a mean convex neighborhood, and are type-I.
