Uniqueness Theorems Of Meromorphic Functions And Meromorphic Mappings In Several Complex Variables

The object of this thesis is to study the uniqueness problems of meromorphic func-tions and meromorphic mappings in several complex variables. Some new uniquenesstheorems are held, which include the following several aspects.Firstly, on the base of the truncated second main theorem for small functions,the multiple values problem of meromorphic functions sharing four small functions isdiscussed. For nonconstant meromorphic functions fⁱ(1≤i≤3) and small functionsa_j(1≤j≤4), assume that the multiplicities of the zero points of fⁱ-a_j withmultiplicities no more than k_j are v_{fⁱ-aj,≤kj}which satisfy v_{f¹-aj,≤kj}²=v_{f²-aj,≤kj}²=v_{f³-aj,≤kj}²,where v_{fⁱ-aj,≤kj}²=min{2, v_{fⁱ-aj,≤kj}}. It is concluded that there exist atmost two distinct meromorphic functions among fⁱ(1≤i≤3), if k_j(1≤j≤4)satisfy one of the following conditions: k₁=…=k₄=15; k₄=14, k₁=k₂=k₃=16; k₄=13, k₁=k₂=k₃=17.Secondly, for meromorphic mappings f, g and hyperplane H, if the zeros set ofinner product (f, H) is contained in that of (g, H), a uniqueness theorem of meromor-phic mappings is proved under this inclusion relation and an additional condition of thecounting functions, which is a generalization of the relative theorem for meromorphicfunctions. The results for moving targets are also obtained.Finally, a weak Cartan-type second main theorem for meromorphic mappings in-tersecting hypersurfaces is given, and a uniqueness theorem is verified by this secondmain theorem, where these meromorphic mappings are algebraically non-degenerate.This is the first time to discuss the uniqueness problem of meromorphic mappings in-tersecting hypersurfaces...