The size of the singular set in mean curvature flow of mean-convex sets

Author:
Brian White

Journal:
J. Amer. Math. Soc. **13** (2000), 665-695

MSC (2000):
Primary 53C44; Secondary 49Q20

DOI:
https://doi.org/10.1090/S0894-0347-00-00338-6

Published electronically:
April 10, 2000

MathSciNet review:
1758759

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that when a compact mean-convex subset of (or of an -dimensional riemannian manifold) moves by mean-curvature, the spacetime singular set has parabolic hausdorff dimension at most . Examples show that this is optimal. We also show that, as , the surface converges to a compact stable minimal hypersurface whose singular set has dimension at most . If , the convergence is everywhere smooth and hence after some time , the moving surface has no singularities

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Additional Information

**Brian White**

Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305

Email:
white@math.stanford.edu

DOI:
https://doi.org/10.1090/S0894-0347-00-00338-6

Keywords:
Mean curvature flow,
mean convex,
singularities

Received by editor(s):
November 16, 1998

Received by editor(s) in revised form:
March 15, 2000

Published electronically:
April 10, 2000

Additional Notes:
The research presented here was partially funded by NSF grant DMS 9803403 and by a Guggenheim Foundation Fellowship.

Article copyright:
© Copyright 2000
American Mathematical Society