Property \((P)\) and Stein neighborhood bases on \(C^1\) domains
For a bounded pseudo-convex domain \(\Omega\) in \(\mathbb C^n\) \((n\geq2)\), whose boundary is of class \(C^k\) \((k\geq1)\), the property \((P)\) means that for every \(M>0\), there exists a smooth plurisubharmonic function \(\lambda\) on \(\overline{\Omega}\) such that \(0\leq \lambda\leq 1\) on \(\overline{\Omega}\) and \(i\partial \overline{\partial}\lambda\geq iM\partial \overline{\partial}|z|^2\) on \( \partial\Omega\). By using an equivalent form of the \((P)\) property, the author shows in this paper that if \(k=1\), then \(\overline \Omega\) has a Stein neighbourhood basis. Thus improving a previous result which Sibony had proved for \(k=3\).
scientific article; zbMATH DE number 5567367