The Decomposition Theorem Of Complete Quasi-Convex Mapping In A Category Of Reinhardt Domain

This thesis is a monographic study of the following Reinhardt domains. Let M = (M₁,M₂,…, M_n) : [0,1]→[0, l]ⁿ be a C²-function, and M_j(0) = 0, M_j(1) = 1, M"_j＞0, c_1jr^pj-1＜M'_j(r)＜c_2jr^pj-1, r∈(0,1), p_j＞2, 1≤j≤n, 0＜c_1j＜c_2j are constants. DefineThen D_m (?) Cⁿ is a convex Reinhardt domain.The paper consists of three chapters: In chapter 1, the correlative backgroundof several complex variables, some notations, defmtions and the resultsare introduced briefly. In chapter 2, some geometrical properties are discussedwhich are related to the domain D_M. Chapter 3 is concerned with the decomposition theorem of normalized biholomorphic complete quasi-convex mappings on D_M.The main results of this thesis are the extension theorems for a normalizedbiholomorphic complete quasi-convex mapping f : D_M→Cⁿ.