On the dynamics of formation of generic singularities of mean curvature flow. (English) Zbl 1539.53107
In this interesting paper, the formation of generic singularities under mean curvature flow is studied by combining different approaches and results, in particular techniques developed by the author and his collaborators. Thanks to these advanced techniques, detailed information when the initial hypersurfaces are close to cylinders, and the important and fundamental results by T. H. Colding and W. P. Minicozzi II [Ann. Math. (2) 182, No. 1, 221–285 (2015; Zbl 1337.53082)] (which included all the generic blow-ups) are obtained. The cases where the rescaled flow converges to the cylinder \(S^1 \times {\mathbb R}^3\) are studied. Lastly the region controlled in [loc. cit.] to find a finer description of a neighborhood of the singularity is extended.
Reviewer: Vincenzo Vespri (Firenze)
MSC:
| 53E10 | Flows related to mean curvature |
| 58J47 | Propagation of singularities; initial value problems on manifolds |
Citations:
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