Deformation of CR-manifolds, minimal points and CR-manifolds with the microlocal analytic extension property
If \(M\) is a smooth CR-manifold (embedded) and \(p\) is a point in \(M\), the author shows how one can deform \(M\) into a smooth CR-manifold \(M_{d}\), letting fixed all the points outside a small truncated cone with vertex in \(p\), such that \(p\) is a minimal point of \(M_{d}\). Thus one is able to get a new proof of the fact that wedge extendability of continuous CR-functions propagates along the CR-orbits of a CR-manifold. The author also shows that if \(M\) is a connected generic (embedded) CR-manifold, each continuous function on \(M\) is a continuous CR-function iff its restriction to each CR-orbit of \(M\) is a CR-function on the orbit. If \(M\) consists of a single orbit, then each continuous CR-function on \(M\) is wedge extendable at any point of \(M\).
scientific article; zbMATH DE number 1191284