本文主要研究C^n中有界凸Reinhardt域B_p上正规化双全纯完全准凸映射的齐次展开式问题,设f(z):Bp→C^n(p>2)是一个正规化双全纯完全准凸映射,k是满足k<p≤k+1的自然数,那么fj(z)=zj+α(j2)zj^2+…+α(jk)zj^k+O(|z|~(K+1)),其中fj是f的第j个分量,j=1,2….,n.
This paper deals with homogeneous expansion of complete quasiconvex mappings on bounded convex Reinhardt domain Bp in Cn. Let f(z) : Bp→ C^n (p 〉 2) be a normalized biholomorphic complete quasiconvex mapping and k be the natural number that satisfies k 〈 p 〈 k + 1. Then fj(z)=zj+α(j2)zj^2+…+α(jk)zj^k+O(|z|~(K+1)),where fj is the j-th component of f ,j=1,2….,n.