Cylindrical tangent flows in mean curvature flow

Abstract

The only non-compact linearly stable singularity models for mean curvature flow are cylindrical, as shown by Colding-Minicozzi. The uniqueness of blowups at singularities modeled on cylinders was established by Colding-Minicozzi. They also proved rigidity results for cylindrical singularities in their earlier work. In this paper, we develop a different approach inspired by Székelyhidi to study cylindrical singularities and prove uniqueness and rigidity results.

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