Construction of convex mappings of \(p\)-balls in \(\mathbb{C}^2\). (English) Zbl 1056.32017
The authors consider biholomorphic mappings \(F\) of the \(p\)-ball \(B_p=\{ (z,w)\in\mathbb{C}^2 : | z| ^p+| w| ^p < 1 \}\), where \(2\leq p < \infty\). In particular, they find conditions under which functions of the form \(F(z,w)=(z+aw^k,w)\), where \(a\in\mathbb{C}\) and \(k\in\mathbb{N}\), and \(F(z,w)=(f(z),g(w))\), where \(f\) and \(g\) are mappings of the unit disk, map \(B_p\) onto convex domains in \(\mathbb{C}^2\).
Reviewer: Martin Chuaqui (Santiago de Chile)
MSC:
| 32H02 | Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables |
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
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