Wedge removability of metrically thin sets and application to the CR-meromorphic extension (Q5953582)

Let \(M\) be a generic CR submanifold of an open subset of \(\mathbb{C}^n.\) A wedge of edge \(M\) at a point \(p\) is an open set in \(\mathbb{C}^n\) of the form \(z+w\) where \(z\) runs in some open neighborhood of \(p\) in \(M\) and \(w\) runs in some truncated open cone in the normal bundle of \(M\) at \(p.\) Under some convexity assumption in terms of the Levi form at \(p,\) the authors prove the existence of a wedge \(W\) of edge \(M\) at \(p\) such that if \(K\) is a closed subset of \(M\) of null codimension 2 Hausdorff measure, every continuous or locally integrable CR function on \(K\) extends holomorphically to \(W.\) As a corollary, the authors show that every CR-meromorphic function defined on \(M\) extends meromorphically to \(W.\)