A planarity estimate for pinched solutions of mean curvature flow (Q2119895)

The general framework of the paper is that of singularity formation in the mean curvature flow. This is a very ample and difficult problem, which has only partial solutions. The main result of the paper states that the blowups of compact solutions to the mean curvature flow in \(\mathbb{R}^{N}\) initially satisfying a pinching condition \(|A|^{2}<c|H|^{2}\) must be of codimension one. Here, \(A\) denotes the second fundamental form, \(H\) the mean curvature and \(c\) is a constant depending on the dimension of the manifold. The paper is deep and very well written.