MEAN CURVATURE FLOW

被引：82

作者：

Colding, Tobias Holck ^{[1
]}

Minicozzi, William P., II ^{[1
]}

Pedersen, Erik Kjaer ^{[2
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Univ Copenhagen, Dept Math, DK-2100 Copenhagen, Denmark

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 52卷 / 02期

基金：

美国国家科学基金会;

关键词：

MINIMIZING RECTIFIABLE CURRENTS; SINGULARITIES; SURFACES; UNIQUENESS; SETS;

D O I：

10.1090/S0273-0979-2015-01468-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the hypersurface is in general or generic position, then we explain what singularities can occur under the flow, what the flow looks like near these singularities, and what this implies for the structure of the singular set. At the end, we will briefly discuss how one may be able to use the flow in low-dimensional topology.

引用

页码：297 / 333

页数：37

共 71 条

[1] ON THE RADIAL BEHAVIOR OF MINIMAL-SURFACES AND THE UNIQUENESS OF THEIR TANGENT-CONES [J].