Generic mean curvature flow I; generic singularities
Name
Colding_Generic mean curvature.pdf
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690.44 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Colding, Tobias
Minicozzi, William
Date Issued
March 2012
Journal
Annals of Mathematics
Publisher
Princeton University Press
Citation
Colding, Tobias, and William Minicozzi. “Generic mean curvature flow I; generic singularities.” Annals of Mathematics 175, no. 2 (March 1, 2012): 755-833.
Version
Author's final manuscript
Abstract
It has long been conjectured that starting at a generic smooth closed embedded surface in R[superscript 3], the mean curvature flow remains smooth until it arrives at a singularity in a neighborhood of which the flow looks like concentric spheres or cylinders. That is, the only singularities of a generic flow are spherical or cylindrical. We will address this conjecture here and in a sequel. The higher dimensional case will be addressed elsewhere. The key to showing this conjecture is to show that shrinking spheres, cylinders, and planes are the only stable self-shrinkers under the mean curvature flow. We prove this here in all dimensions. An easy consequence of this is that every singularity other than spheres and cylinders can be perturbed away.
Description
Author Manuscript August 26, 2009
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4007/annals.2012.175.2.7
