The growth theorem of convex mappings on the unit ball in ℂⁿ

Abstract

Let ‖ ⋅ ‖ \Vert \cdot \Vert be an arbitrary norm on C n {\mathbb {C}}^{n} . Let f f be a normalized biholomorphic convex mapping on the unit ball in C n {\mathbb {C}}^{n} with respect to the norm ‖ ⋅ ‖ \Vert \cdot \Vert . We will give an upper bound of the growth of f f .