多复变数完全拟凸映射的分解定理

DECOMPOSITION THEOREM OF COMPLETE QUASICONVEX MAPPINGS IN C^n

设Ω_1C^(n1),Ω_2C^(n2)为凸的Reinhardt域,f(z,w)=(f1(z,w),f2(z,w))'为Ω_1×Ω_2上的正规化全纯映射.本文证明f为Ω_1×Ω_2上的正规化双全纯完全拟凸映射当且仅当 f(z,w)=(Φ_1(z),Φ_2(w))'其中φj:Ωj→C^(nj)是Ωj(j=1,2)上的正规化双全纯完全拟凸映射。

Let Cn1,Ω2 C Cn2 be bounded convex Reinhardt domains, f(z,w) = (f1(z,w), f2(z, w))' is a normalized holomorphic mapping on Ω1×Ω)2. Then f is a normalized biholomorphic complete quasiconvex mapping on Ω1×Ω2 if and only if f(z,w) = (φ1 (z),φ2(w))', where φj:Ωj -Cnj is a normalized biholomorphic complete quasiconvex mapping on Ωj (j=1,2).