Liouville rigidity and time-extrinsic Harnack estimates for an anisotropic slow diffusion

We prove that ancient non-negative solutions a fully anisotropic equation are constant if they satisfy a condition of finite speed of propagation and if they are both one-sided bounded, and bounded in $\R^N$ at a single time level. A similar statement is valid when the bound is given at a single space point. As a general paradigm, H\"older estimates provide the basics for rigidity. Finally, we show that recent intrinsic Harnack estimates can be improved to an Harnack inequality valid for non-intrinsic times. Locally, they are equivalent.