Ancient mean curvature flows that converge rapidly to a compact self-shrinker at time minus infinity must have the same codimension as the shrinker, and if the convergence is super-exponential the flow equals the shrinker.
Uniqueness of convex ancient solutions to mean curvature flow in R^3
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Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at $-\infty$
Ancient mean curvature flows that converge rapidly to a compact self-shrinker at time minus infinity must have the same codimension as the shrinker, and if the convergence is super-exponential the flow equals the shrinker.