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In this note we announce results on the mean curvature flow of mean-convex sets in three dimensions. Loosely speaking, our results justify the naive picture of mean curvature flow where the only singularities are neck pinches, and components which collapse to asymptotically round spheres.

Copyright 2003 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 09 (2003), pp. 121-124
• Publisher Identifier: S 1079-6762(03)00119-7
• 2000 Mathematics Subject Classification. Primary 53C44
• Key words and phrases. Mean-convex, mean curvature, singularities
• Received by editors September 24, 2003
• Posted on November 26, 2003
• Communicated by Svetlana Katok
• Comments (When Available)

Tobias H. Colding

Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012

E-mail address: colding@cims.nyu.edu

Bruce Kleiner

Department of Mathematics, University of Michigan, 2072 East Hall, 525 E University Avenue, Ann Arbor, Michigan 48109-1109

E-mail address: bkleiner@umich.edu

The first author was supported by NSF grant DMS-0104453 The second author was supported by NSF grant DMS-0204506.