Nonfattening of Mean Curvature Flow at Singularities of Mean Convex Type
Nonfattening of Mean Curvature Flow at Singularities of Mean Convex Type
复制标题
平均凸型奇点处平均曲率流的去肥化
DOI：
10.1002/cpa.21852
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发表时间：
2017
影响因子：
3
通讯作者：
B. White
中科院分区：
文献类型：
--
作者：
Or Hershkovits;B. White
我们证明了从一个紧致的光滑嵌入超曲面M n + 1出发的平均曲率流保持唯一的过去奇点，只要奇点是平均凸型的，即，如果围绕每个奇点，则曲面沿一个方向移动。具体地说，M的水平集流不胖，如果所有的奇点的平均凸型。我们进一步证明了定理的假设成立，只要所有的爆破流都是出现在平均凸流中的那种，即，光滑、重数1和凸。我们的结果推广了一个众所周知的事实，即平均凸初始超曲面M的水平集流不会变胖。他们还提供了第一个实例，其中nonfattening的结论，从当地的信息周围的奇异集或从信息的奇异性配置文件的流量。© 2019 Wiley Periodicals，Inc.
We show that a mean curvature flow starting from a compact, smoothly embedded hypersurface M ⊆ ℝn + 1 remains unique past singularities, provided the singularities are of mean convex type, i.e., if around each singular point, the surface moves in one direction. Specifically, the level set flow of M does not fatten if all singularities are of mean convex type. We further show that assumptions of the theorem hold provided all blowup flows are of the kind appearing in a mean convex flow, i.e., smooth, multiplicity 1, and convex. Our results generalize the well‐known fact that the level set flow of a mean convex initial hypersurface M does not fatten. They also provide the first instance where nonfattening is concluded from local information around the singular set or from information about the singularity profiles of a flow. © 2019 Wiley Periodicals, Inc.