an:05606096
Zbl 1186.31001
Oh, Chun-Young
A simple note on Hartogs-Laurent domain
EN
Honam Math. J. 30, No. 2, 359-362 (2008).
00250860
2008
j
31A05 32V05
\(E_*\)-extension property; Hartogs-Laurent domain; taut domain
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 \(\mathbb C^n\).
Theodore J. Barth (Riverside)