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 | References | Similar Articles | Additional Information

Abstract: This paper analyzes the singular behavior of the mean curvature flow generated by the boundary of the compact mean-convex region of or of an -dimensional riemannian manifold. If , 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 , 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