On unicity problems of meromorphic mappings of Cn into PN(C) and the ramification of the Gauss maps of complete minimal surfaces

• Main Author: Ha, Pham Hoang
• Language: ENG
• Published: Université de Bretagne occidentale - Brest 2013
• Subjects: [MATH:MATH_GM] Mathematics/General Mathematics; Value distribution theory; Second main theorem; Unicity theorem; Meromorphic mappng; Minimal surface; Gauss map; Ramification
• Online Access: http://tel.archives-ouvertes.fr/tel-00871320; http://tel.archives-ouvertes.fr/docs/00/87/13/20/PDF/These-2013-SICMA-Mathematiques-HA_Pham_Hoang.pdf

In 1975, H. Fujimoto generalized Nevanlinna's known results for meromorphic fonctions to the case of meromorphic mappings of Cn into PN(C). He proved that for two linearly nondegenerate meromorphic mappings f and g of C into PN(C). if they have the saine inverse images counted with multiplicities for 3N + 2 hyperplanes in general position in PN(C) then f = g. After that, this problem has been studied intensively by a number of mathematicans as H. Fujimoto, W. Stoll, L. Smiley, M. Ru, G. Dethloff - T. V. Tan, D. D. Thai - S. D. Quang, Chen-Yan and so on. Parallel to the development of Nevanlinna theory, the value distribution theory of the Gauss map of minimal surfaces immersed in Rm vas studied by many mathematicans as R. Osserman, S.S. Chern, F. Xavier, H. Fujimoto, S. J. Kao, M. Ru and many other mathematicans. In this thesis, we continuous studing some problems on these directions. The main goals of the thesis are followings. * Unicity theorems with truncated multiplicities of meromorphic mappings of Cn into PN(C) sharing 2N + 2 fixed hyperplanes.* Unicity theorems with truncated multiplicities of meromorphic mappings of Cn into PN(C) for moving targets, and a small set of identity.