Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)



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
Published electronically: April 10, 2000
MathSciNet review: 1758759
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that when a compact mean-convex subset of $\mathbf {R}^{n+1}$ (or of an $(n+1)$-dimensional riemannian manifold) moves by mean-curvature, the spacetime singular set has parabolic hausdorff dimension at most $n-1$. Examples show that this is optimal. We also show that, as $t\to \infty$, the surface converges to a compact stable minimal hypersurface whose singular set has dimension at most $n - 7$. If $n < 7$, the convergence is everywhere smooth and hence after some time $T$, the moving surface has no singularities

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 53C44, 49Q20

Retrieve articles in all journals with MSC (2000): 53C44, 49Q20

Additional Information

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

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