Geodesic
Singularity structure in mean curvature flow of mean-convex sets
Colding, Tobias1 ; Kleiner, Bruce2
1 Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
2 Department of Mathematics, University of Michigan, 2072 East Hall, 525 E University Avenue, Ann Arbor, Michigan 48109-1109
Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 121-124 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S1079-6762-03-00119-7

Colding, Tobias 1 ; Kleiner, Bruce 2

1 Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
2 Department of Mathematics, University of Michigan, 2072 East Hall, 525 E University Avenue, Ann Arbor, Michigan 48109-1109 
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Colding, Tobias; Kleiner, Bruce. Singularity structure in mean curvature flow of mean-convex sets. Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 121-124. doi: 10.1090/S1079-6762-03-00119-7

[1] Brakke, Kenneth A. The motion of a surface by its mean curvature 1978

[2] Chen, Yun Gang, Giga, Yoshikazu, Goto, Shun’Ichi Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations J. Differential Geom. 1991 749 786

[3] Evans, L. C., Spruck, J. Motion of level sets by mean curvature. I J. Differential Geom. 1991 635 681

[4] Huisken, Gerhard, Sinestrari, Carlo Convexity estimates for mean curvature flow and singularities of mean convex surfaces Acta Math. 1999 45 70

[5] Huisken, Gerhard, Sinestrari, Carlo Mean curvature flow singularities for mean convex surfaces Calc. Var. Partial Differential Equations 1999 1 14

[6] Ilmanen, Tom Elliptic regularization and partial regularity for motion by mean curvature Mem. Amer. Math. Soc. 1994

[7] Kober, Hermann Transformationen von algebraischem Typ Ann. of Math. (2) 1939 549 559

[8] White, Brian The size of the singular set in mean curvature flow of mean-convex sets J. Amer. Math. Soc. 2000 665 695

[9] White, Brian The nature of singularities in mean curvature flow of mean-convex sets J. Amer. Math. Soc. 2003 123 138

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