We prove several sharp one-sided pinching estimates for immersed and embedded hypersurfaces evolving by various fully nonlinear, one-homogeneous curvature flows by the method of Stampacchia iteration. These include sharp estimates for the largest principal curvature and the inscribed curvature (“cylindrical estimates”) for flows by concave speeds and a sharp estimate for the exscribed curvature for flows by convex speeds. Making use of a recent idea of Huisken and Sinestrari, we then obtain corresponding estimates for ancient solutions. In particular, this leads to various characterisations of the shrinking sphere amongst ancient solutions of these flows.

中文翻译：

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完全非线性曲率流的锋利的单侧曲率估计以及在古代求解中的应用

我们通过Stampacchia迭代方法证明了由各种完全非线性的，一阶曲率流演变而来的沉浸式和嵌入式超曲面的几个尖锐的单边收缩估计。这些包括通过凹面速度对最大主曲率和内接曲率的敏锐估计（“圆柱估计”）和对凸面速度对流体的内切曲率的敏锐估计。利用Huisken和Sinestrari的最新思想，我们可以得到相应的古代解的估计。特别是，这导致了这些流动的古老解决方案中不断缩小的领域的各种特征。