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

White, Brian

doi:10.1090/S0894-0347-02-00406-X

The nature of singularities in mean curvature flow of mean-convex sets
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by Brian White

J. Amer. Math. Soc. 16 (2003), 123-138

DOI: https://doi.org/10.1090/S0894-0347-02-00406-X

Published electronically: October 9, 2002

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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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