  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.
