Extending CR functions from manifolds with boundaries (Q1910660)

This paper is concerned with the extendibility of \(CR\) functions defined on manifolds with edges. Let \(M\subset \mathbb{C}^N\) be on smooth generic manifold with generic edge \(M_0\). Let \(p\in M_0\). The author introduces the concept of defect of \(M\) at \(p\). This defect, henceforth denoted by \(d\), involves the limiting defects of analytic discs attached to \(M \cup M_0\) and passing through \(p\). The main results of the paper are the following: A. There is a manifold \(W\) with edge \(M_0\) and \(\dim W=2 N-d\) such that all \(CR\) functions on \(M \cup M_0\) extend to \(CR\) functions on \(W \cup M_0\). B. Near \(p\) there is a closed \(CR\) submanifold \(S\subset M\) with edge \(S_0=M_0 \cap \overline S\) such that \(p\in S_0\), \(\dim S= \dim M-d\) and \(CR\dim S= CR \dim M\). The author points out that if \(M\) is minimal at \(P\) then it follows from \(B\) that \(d=0\). But then \(A\) implies that all \(CR\) functions on \(M\cup M_0\) extend to \(CR\) functions on a wedge (full dimensional manifold) with edge \(M_0\).