Extension of holomorphic functions through a hypersurface by tangent analytic discs (Q1423454)

Let \(\Omega\) be a domain in \(\mathbb{C}^n\) with boundary \(M\), and \(A\) an analytic disc attached to \(\overline\Omega\) and not to \(M\), i.e., \(\partial A\subset\overline\Omega\) but \(\partial A\not\subset M\). Assume \(A\) is tangent to \(M\) at a point \(z^0\in\partial A\cap M\). The author proves that if \(B\) is a ball with center \(z^0\) such that \(B\supset\overline A\), then any holomorphic function \(f\) on \(\Omega\cap B\) extends holomorphically to a fixed neighborhood of \(z^0\). For the proof the author uses the properties of superharmonicity of \(\log r^\nu_f\), where \(r^\nu_f\) denotes the radius of convergence of the Taylor series of a holomorphic function \(f\) on \(\Omega\) in a direction \(\nu\in \mathbb{C}^n\setminus\{0\}\).