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Mean curvature flow

Author(s)
Colding, Tobias; Minicozzi, William; Pedersen, Erik J
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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Abstract
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.
Date issued
2015-01
URI
http://hdl.handle.net/1721.1/110410
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Mathematics
Journal
Bulletin of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Citation
Colding, Tobias Holck, William P. Minicozzi, and Erik Kjær Pedersen. “Mean Curvature Flow.” Bulletin of the American Mathematical Society 52.2 (2015): 297–333. © 2015 American Mathematical Society
Version: Final published version
ISSN
0273-0979
1088-9485

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