Mean curvature flow

• Main Authors: Colding, Tobias (Contributor), Minicozzi, William (Contributor), Pedersen, Erik J (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor), Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: American Mathematical Society (AMS), 2017-06-30T23:22:02Z.
• Subjects: Article
• Online Access: Get fulltext

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.
National Science Foundation (U.S.) (Grant DMS 11040934)
National Science Foundation (U.S.) (Grant DMS 0906233)
National Science Foundation (U.S.). Focused Research Group (Grant DMS 0854774)
National Science Foundation (U.S.). Focused Research Group (Grant DMS 0853501)