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

Hamada, Hidetaka

doi:10.1090/S0002-9939-99-04964-3

The growth theorem of convex mappings on the unit ball in $\mathbb {C}^n$
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Proc. Amer. Math. Soc. 127 (1999), 1075-1077 Request permission

Abstract:

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

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