Harnack inequality and pinching estimates for anisotropic curvature flow of hypersurfaces

We obtain a differential Harnack inequality for anisotropic curvature flow of convex hypersurfaces in Euclidean space with its speed given by a curvature function of homogeneity degree one in a certain class, and restrictions depending only on the initial data and the anisotropic factor which reflects the influence of the ambient space. Moreover, the pinching estimate for such flows is derived from the maximum principle for tensors.