  Second derivative pinching estimates are proved for a class of elliptic and
parabolic equations, including motion of hypersurfaces by curvature functions
such as quotients of elementary symmetric functions of curvature. The estimates
imply convergence of convex hypersurfaces to spheres under these flows,
improving earlier results of B. Chow and the author. The result is obtained via
a detailed analysis of gradient terms in the equations satisfied by second
derivatives.
