Treffer: ON EXTENSION OF ANALYTIC SETS THROUGH GENERIC MANIFOLDS: On extension of analytic sets through generic manifolds

Let \(M\) be a generic \({\mathbf R}\)-analytic submanifold of a domain \(\Omega\subset {\mathbf C}^ n\) of real codimension at least 2, and let \(A\) be a complex \(p\)-dimensional submanifold of \(\Omega\setminus M\) whose boundary in \(\Omega\) is \(bA\). Suppose that the pair \((A,bA)\) is a \({\mathcal C}^ 1\)-manifold with boundary and that the manifolds \(A\), \(M\) are Levi- transversal at a point \(a\in bA\). The author proves that \(A\) can be extended to a complex manifold in a neighbourhood of the point \(a\). [See also the author, Mat. Zametki 46, No.1, 119 (1989; see the paper above)].