Cylindrical tangent flows in mean curvature flow

TL;DR

This paper proves the uniqueness of cylindrical tangent flows in mean curvature flow using a novel approach inspired by Székelyhidi, building on prior work that identified cylinders as the only stable singularity models.

Contribution

It introduces a new proof technique for the uniqueness of cylindrical tangent flows in mean curvature flow, differing from previous methods.

Findings

Confirmed the uniqueness of cylindrical tangent flows using a Székelyhidi-inspired approach.

Extended understanding of singularity models in mean curvature flow.

Provided a new method that could be applied to other geometric flow problems.

Abstract

The only non-compact linearly stable singularity models for mean curvature flow are cylindrical by Colding-Minicozzi. The uniqueness of blowups at singularities modeled on the cylinders has been established by the same authors. In this paper, we will use a different approach inspired by Sz\'ekelyhidi to prove the uniqueness result.