Tangent discs and extension of CR functions to wedges of \({\mathbb C}^n\)
The authors consider the problem of propagation of extendability for CR functions. They consider an edge \(N\) of a generic wedge \(V\), contained in a CR submanifold \(M\) of \(\mathbb C^n\). They show that if \(p_0\in N\), \(p_1\in V\) belongs to the boundary of a same analytic disc attached to \(V\cup N\), then any CR function on \(V\) which CR extends at \(p_1\) in a direction normal to \(M\) also CR extends in \(p_0\) to a direction normal to \(N\) and transversal to \(M\). The two directions of the extensions are related by an \(m\times m\)-matrix \(\lambda\) associated to the analytic disc (\(m\) is the CR codimension of \(M\)). As an application, they obtain another proof of \textit{A. Tumanov}'s propagation of the extendability theorem [Contemp. Math. 205, 259-269 (1997; Zbl 0883.32011)].
scientific article; zbMATH DE number 1777192
scientific article