Uniqueness problem of meromorphic mappings from a complete K\"{a}hler   manifold into a projective variety
  The purpose of this paper has twofold. The first is to prove a unicity theorem for meromorphic mappings of a complete K\"{a}hler manifold M in P^n(C) sharing few hypersurfaces. The second is to give a unicity theorem for the case of differential nondegenerate meromorphic mappings sharing 2N-n+3+2\rho(2N-n+1) hyperplanes in N subgeneral position. 
Le Ngoc Quynh
math.CV