Some gradient estimates and Liouville properties of the fast diffusion equation on Riemannian manifolds (Q2047227)

Let \(\Delta_t\) be the Laplacian associated with a Ricci flow and consider the fast diffusion equation \[\partial_t u_t= \Delta_t u_t^\alpha\] for \(\alpha\in (0,1).\) The Li-Yau type gradient estimate as well as Liouville theorem are established for positive solutions to this equation, which extend some existing results derived for the heat equation where \(\alpha=1\).