Uniqueness of conical singularities for mean curvature flows

TL;DR

This paper establishes the uniqueness of asymptotically conical tangent flows in mean curvature flow across all codimensions, extending previous results from hypersurfaces to higher codimensions.

Contribution

It generalizes the uniqueness of conical singularities in mean curvature flows from hypersurfaces to all codimensions, building on earlier work.

Findings

Proves uniqueness of asymptotically conical tangent flows in all codimensions.

Extends prior hypersurface results to higher codimensions.

Provides a comprehensive framework for understanding singularities in mean curvature flows.

Abstract

In this paper, we prove the uniqueness of asymptotically conical tangent flows in all codimensions. This is based on an early work of Chodosh-Schulze, who proved the uniqueness in the hypersurface case.