A correction to ``The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function''
The main result of the author's previous paper [ibid. 6, 687-703 (1998; Zbl 0923.31005)] is Theorem 1.2 which states that the pluricomplex Green function of a smooth, bounded, strongly pseudoconvex domain \(\Omega\subset \mathbb{C}^n\) with a logarithmic pole at \(\zeta\in\Omega\) belongs to \(C^{1,\alpha}(\overline\Omega\setminus \{\zeta\})\) for any \(\alpha\in (0,1)\). In the present note, the author indicates that the proof of that theorem is incomplete because it makes use of Lemma 3.1 whose proof contains an error. A new proof of Theorem 1.2 independent of Lemma 3.1 is presented.
scientific article; zbMATH DE number 1423043