Mean curvature flow

TY - JOUR

T1 - Mean curvature flow

AU - Colding, Tobias Holck

AU - Minicozzi II, William P.

AU - Pedersen, Erik Kjær

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

M3 - Journal article

SN - 0273-0979

VL - 52

SP - 297

EP - 333

JO - Bulletin of the American Mathematical Society

JF - Bulletin of the American Mathematical Society

IS - 2

ER -