Mean curvature flow
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- by Tobias Holck Colding, William P. Minicozzi II and Erik Kjær Pedersen PDF
- Bull. Amer. Math. Soc. 52 (2015), 297-333 Request permission
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.References
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Additional Information
- Tobias Holck Colding
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachu- setts Avenue, Cambridge, Mssachusetts 02139-4307
- MR Author ID: 335440
- Email: colding@math.mit.edu
- William P. Minicozzi II
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachu- setts Avenue, Cambridge, Mssachusetts 02139-4307
- MR Author ID: 358534
- Email: minicozz@math.mit.edu
- Erik Kjær Pedersen
- Affiliation: Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
- Email: erik@math.ku.dk
- Received by editor(s): August 27, 2012
- Received by editor(s) in revised form: June 11, 2014
- Published electronically: January 13, 2015
- Additional Notes: The first two authors were partially supported by NSF Grants DMS 11040934, DMS 0906233, and NSF FRG grants DMS 0854774 and DMS 0853501
- © Copyright 2015 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 52 (2015), 297-333
- MSC (2010): Primary 53C44
- DOI: https://doi.org/10.1090/S0273-0979-2015-01468-0
- MathSciNet review: 3312634