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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 nature of singularities in mean curvature flow of mean-convex sets
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by Brian White PDF
J. Amer. Math. Soc. 16 (2003), 123-138 Request permission

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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Additional Information
  • Brian White
  • Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-2060
  • Email: white@math.stanford.edu
  • 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.
  • © Copyright 2002 American Mathematical Society
  • 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
  • MathSciNet review: 1937202