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A simple note on Hartogs-Laurent domain. (English) Zbl 1186.31001
Let \(u : \mathbb C \rightarrow \mathbb R\) be a continuous subharmonic function satisfying \(\lim_{|z| \rightarrow \infty} u(z) = \infty\). The author proves that the domain \(0 < |w| e^{u(z)} < 1\) in \(\mathbb C^2\) is taut. Contrary to an assertion in this paper, the continuity assumption cannot be replaced with the weaker condition that \(u\) be bounded below. The author also studies questions about extending holomorphic maps from the punctured unit disk into a Hartogs-Laurent domain \(e^{\psi (z)} < |w| < e^{-\phi (z)}\) where \(\phi\) and \(\psi\) are plurisubharmonic functions satisfying \(\phi + \psi < 0\) on a domain \(G\) in \(\mathbb C^n\).
MSC:
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
32V05 CR structures, CR operators, and generalizations
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