The Second Main Theorem Of Meromorphic Mapping And Its Applications

The value distribution theory of meromorphic mappping into projective space and its applications are studied in this thesis.The main research tools are Nevanlinna theory,differential geometry and algebraic geometry.On the one hand,We obtain the second main theorem of non-degenerate with weighted coefficient and its applications,the problems of uniqueness and algebraic dependence.On the other hand,we research the second main theorem of Gauss mapping on a compact Riemann minimal surface and its applications.The content of the paper is arranged as follows:In chapter 1,introduces the research background in Nevanlinna theory and its analysis of the significance.In chapter 2,introduces some basic concepts in Nevanlinna theory.In chapter 3,we proved some new second main theorem for meromorphic mappings into complex projective space with the truncated counting function has different weighted and proves the algebraic dependence theorem with it.In chapter 4,we obtain the second main theorem for algebraic curves from compact Riemann surfaces into the complex projective space which is ramified over hypersurfaces in subgeneral position.And we get the ramification and unicity problem for the generalized gauss map of complete regular minimal surfaces with finite total curvature.In chapter 5,we give the summary and prospect.On the one hand,we summarized this article,on the other hand some unresolved problem are put forward.