Cylindrical estimates for hypersurfaces moving by convex curvature functions (Q459055)

The authors prove a complete family of cylindrical estimates for solutions of a class of fully nonlinear curvature flows which generalize the cylindrical estimate of \textit{G. Huisken} and \textit{C. Sinestrari} [Invent. Math. 175, No. 1, 137--221 (2009; Zbl 1170.53042)] for the mean curvature flow. More precisely they show that for the class of flows considered, at points where the curvature is becoming large, an \((m+1)\)-convex (\(0\leq m\leq n-2\)) solution either becomes strictly \(m\)-convex or its Weingarten map becomes that of a cylinder \(\mathbb{R}^m\times S^{n-m}\). This result complements the convexity estimate they proved with McCoy before for the same class of flows.