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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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