Weighted pluripotential theory on complex K\"{a}hler manifolds
  We introduce a weighted version of the pluripotential theory on complex K\"{a}hler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its behaviour under holomorphic maps. We also establish a generalization of Siciak's H-principle. 
Maritza M. Branker, Malgorzata Stawiska