Decay order bound for mean curvature flow near compact singularities

TL;DR

This paper establishes a uniform bound on the decay order of rescaled mean curvature flows near compact singularities, leading to a unique continuation result, advancing understanding of singularity behavior in geometric flows.

Contribution

It introduces a bound on the decay order for rescaled flows near singularities and proves a related unique continuation property, providing new insights into singularity analysis in mean curvature flow.

Findings

Decay order of rescaled flow is uniformly bounded.

Unique continuation property for flows near singularities.

Enhanced understanding of singularity structure in mean curvature flow.

Abstract

We consider the rescaled flow associated with a mean curvature flow that develops a compact singularity of multiplicity one. We prove that the ``decay order'' of such a rescaled flow is uniformly bounded. As a consequence, we prove a unique continuation result.