Subordination chains and biholomorphic mappings on bounded balanced pseudoconvex domains

Let ΩΩ be a bounded balanced pseudoconvex domain with C1C1 plurisubharmonic defining functions in CnCn and let f(z,t)f(z,t) be a univalent subordination chain such that z=0z=0 is a zero of order k+1k+1 of e−tf(z,t)−z for each t≥0t≥0. In this paper, we study several properties for f(⋅,0)f(⋅,0), concerning the growth, covering theorems and coefficient bounds. These results generalize the related works of Hamada and Kohr.