论文标题
cylindrical Selfrinkers的不平等现象，独特性和刚性
Łojasiewicz inequalities, uniqueness and rigidity for cylindrical self-shrinkers
论文作者
论文摘要
我们为平均曲率流动的一类圆柱体自我碎裂器建立了lojasiewicz的不平等，其中包括任何编码符号，其中包括圆缸和圆柱体在abresch-ranger曲线上。我们推断出在这类圆柱体上建模的奇异性上的爆炸的独特性，并在自我缩短器的空间中孤立了任何此类圆柱体。 Abresch-Stranger案回答了一种猜想。我们的证明使用了收缩器平均曲率的直接扰动分析，因此即使对于圆形圆柱体也是新的。
We establish Łojasiewicz inequalities for a class of cylindrical self-shrinkers for the mean curvature flow, which includes round cylinders and cylinders over Abresch-Langer curves, in any codimension. We deduce the uniqueness of blowups at singularities modelled on this class of cylinders, and that any such cylinder is isolated in the space of self-shrinkers. The Abresch-Langer case answers a conjecture of Colding-Minicozzi. Our proof uses direct perturbative analysis of the shrinker mean curvature, so it is new even for round cylinders.
