Hamilton-Souplet-Zhang type gradient estimates for porous medium type   equations on Riemannian manifolds
  In this paper, by employ the cutoff function and the maximum principle, some Hamilton-Souplet-Zhang type gradient estimates for porous medium type equation are deduced. As a special case, an Hamilton-Souplet-Zhang type gradient estimates of the heat equation is derived which is different from the result of Souplet-Zhang.   Furthermore, our results generalize those of Zhu. As application, some Livillous theorems for ancient solution are derived. 
Wen Wang
math.DG