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Planarity estimates and codimension reduction for ancient flows at the Andrews-Baker threshold
We derive an interior planarity estimate for space-time proper mean curvature flows of $n$-dimensional submanifolds of $\mathbb R^{n+p}$, $n\geq5$, that are uniformly quadratically pinched up to the Andrews-Baker threshold $\frac{4}{3n}$. The estimate is parabolically scale-invariant and it requires
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