One-sided ancient mean curvature flow


We discuss about uniqueness of ancient mean curvature flow whose rescaled flow stays in a one-side of a shrinker. The rescaled flow locally and smoothly converges to the shrinker as time goes back. Hence, the flow is the graph of a positive function defined on the shrinker. Therefor, a parabolic Liouville’s theorem for positive entire ancient solutions gives us the uniqueness.