Tumanov, A. E. Extension of CR-functions into a wedge. (Russian) Zbl 0714.32005 Mat. Sb. 181, No. 7, 951-964 (1990). Let a manifold \(M\subset {\mathbb{C}}^{n+m}\) in a neighbourhood of the origin be given by the equation \(x=h(y,w)\), where \(z=x+iy\in {\mathbb{C}}^ m,\) \(w\in {\mathbb{C}}^ n\), h be a smooth function in a neighbourhood of the origin of \({\mathbb{R}}^ m\times {\mathbb{C}}^ m\) with its values in \({\mathbb{R}}^ m\), \(h(0,0)=0\), \(dh(0,0)=0\). A set \({\mathcal M}_ r(U,{\mathbb{C}})=\{(z,w)\in U\), x-h(y,w)\(\in {\mathbb{C}}\}\) is said to be a wedge of range r with the edge M if U is a non-singular surface of dimension \(2n+m+r\) which contains some neighbourhood of the origin on M and \({\mathbb{C}}\) is an open convex cone in \({\mathbb{R}}^ m\). The manifold M is said to admit a \(W_ r\)-extension in a point \(p\in M\) if one can choose such coordinates (z,w) with the origin in p, a surface M and a cone \({\mathbb{C}}\) that every continuous CR-function on M admits a continuous CR- extension to \({\mathcal M}_ r(U,{\mathbb{C}}).\) The author studies conditions of the existence of \(W_ r\)-extensions. One of the results obtained is as follows. Theorem 1. Let M admit no \(W_ r\)-extension in a point \(p\in M\) for some r, \(1\leq r\leq m\). Then there exists a CR-submanifold \(N\subset M\), \(p\in N\), CR-dim N\(=n\), \(\dim N<2n+r\). Reviewer: L.Ronkin Cited in 1 ReviewCited in 18 Documents MSC: 32V40 Real submanifolds in complex manifolds Keywords:wedge; CR-function; CR-extension PDFBibTeX XMLCite \textit{A. E. Tumanov}, Mat. Sb. 181, No. 7, 951--964 (1990; Zbl 0714.32005) Full Text: EuDML