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The nature of singularities in mean curvature flow of mean-convex sets


Author: Brian White
Journal: J. Amer. Math. Soc. 16 (2003), 123-138
MSC (2000): Primary 53C44; Secondary 49Q20
DOI: https://doi.org/10.1090/S0894-0347-02-00406-X
Published electronically: October 9, 2002
MathSciNet review: 1937202
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Abstract: This paper analyzes the singular behavior of the mean curvature flow generated by the boundary of the compact mean-convex region of $\mathbf{R}^{n+1}$ or of an $(n+1)$-dimensional riemannian manifold. If $n<7$, the moving boundary is shown to be very nearly convex in a spacetime neighborhood of any singularity. In particular, the tangent flows at singular points are all shrinking spheres or shrinking cylinders. If $n\ge 7$, the same results are shown up to the first time that singularities occur.


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Additional Information

Brian White
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-2060
Email: white@math.stanford.edu

DOI: https://doi.org/10.1090/S0894-0347-02-00406-X
Keywords: Mean curvature flow, mean convex, singularity
Received by editor(s): November 25, 1998
Received by editor(s) in revised form: September 11, 2002
Published electronically: October 9, 2002
Additional Notes: The research presented here was partially funded by NSF grants DMS 9803403, DMS 0104049, and by a Guggenheim Foundation Fellowship.
Article copyright: © Copyright 2002 American Mathematical Society

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