摘要：In this talk, I will discuss recent work with Ben Andrews and James McCoy in which the analogous estimates are obtained for a large class of fully non-linear curvature flows. Our methods streamline those of Huisken and Sinestrari and, in particular, provide a simpler proof of the Huisken-Sinestrari convexity estimate. Moreover, we are able to obtain an entire family cylindrical estimates: For any (k+1)-convex solution (so that the sum of the smallest $k+1$ principal curvatures is always positive), either the Weingarten map is $k$-positive, or close to the Weingarten map of a cylinder, $\R^k\times S^{n-k}$, of small radius, at any point where the mean curvature is large.