Distortion theorems for convex mappings on homogeneous balls (Q984696)

The authors prove a distorsion theorem for normalized holomorphic convex maps defined on a homogeneous unit ball \(B\) of a complex Banach space~\(X\), where a holomorphic map \(f: B\to X\) is normalized if \(f(O)=O\) and \(df_O=\text{id}\), and it is convex if it is a biholomorphism and its image is convex. Under these hypotheses, the authors give lower and upper bounds both for the norm of the differential \(df\) and for the distance \(\|f(a)-f(b)\|\) between two points in the image, generalizing various finite-dimensional distorsion theorems.