Mean curvature flow
Name
Colding_Mean curvature.pdf
Size
4.33 MB
Format
Adobe PDF
Checksum (MD5)
c69abdf2ef2836bb2a271f3c5522ddd2
Author(s)
Colding, Tobias
Minicozzi, William
Pedersen, Erik J
Date Issued
January 2015
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1090/S0273-0979-2015-01468-0
