Liouville-type theorems on the complete gradient shrinking Ricci   solitons
  We prove that there does not exist non-constant positive $f$-harmonic function on the complete gradient shrinking Ricci solitons. We also prove the $L^{p}(p\geq 1 \ {\rm or}\ 0<p\leq 1)$ Liouville theorems on the complete gradient shrinking Ricci solitons. 
Huabin Ge, Shijin Zhang
math.DG