The growth theorem for biholomorphic mappings in several complex variables (Q5905425)

A growth theorem of normalized biholomorphic starlike mapping on classical domains is proved here. The result obtained is: Let \(W=f(Z)\) be a normalized biholomorphic starlike mapping on classical domains \(R_ K\) \((K=I,II,III,IV)\), which maps \(R_ K\) to \(C^{\dim R_ K}\). Then \[ | z|/(1+\| z\|_ K)^ 2\leq| f(z)|\leq| z|/(1-\| z\|_ K)^ 2 \] holds for every \(Z\in R_ K\).