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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The size of the singular set in mean curvature flow of mean-convex sets
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by Brian White PDF
J. Amer. Math. Soc. 13 (2000), 665-695 Request permission

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
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Additional Information
  • Brian White
  • Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
  • Email: white@math.stanford.edu
  • 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.
  • © Copyright 2000 American Mathematical Society
  • 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
  • MathSciNet review: 1758759