Finite jet determination of holomorphic mappings at the boundary
Abstract
Description
Let M,M' be smooth real hypersurfaces in N-dimensional space and assume that M is k-nondegenerate at a point p in M. We prove that holomorphic mappings that extend smoothly to M, sending a neighborhood of p in M diffeomorphically into M' are completely determined by their 2k-jet at p. As an application of this result, we also give sufficient conditions on a smooth real hypersurface which guarantee that the space of infinitesimal CR automorphisms is finite dimensional.
27 pages; AMS-TeX; In this revised version, a result showing that smooth CR diffeomorphisms depend smoothly on their jets of a certain predetermined order has been added. Some corrections have also been made
27 pages; AMS-TeX; In this revised version, a result showing that smooth CR diffeomorphisms depend smoothly on their jets of a certain predetermined order has been added. Some corrections have also been made