Generating Shrinkers by Mean Curvature Flow

TL;DR

This paper proves the existence of certain shrinkers in mean curvature flow by constructing compact, embedded surfaces that develop singularities, providing new examples of these geometric objects.

Contribution

It introduces a method to produce new shrinkers by analyzing mean curvature flow and singularity formation.

Findings

Constructed new examples of shrinkers as blowup limits.

Demonstrated existence of smooth, embedded surfaces leading to singularities.

Enhanced understanding of singularity models in mean curvature flow.

Abstract

We prove existence for many examples of shrinkers by producing compact, smoothly embedded surfaces that, under mean curvature flow, develop singularities at which the shrinkers occur as blowups.