Finite jet determination of holomorphic mappings at the boundary

Details Finite jet determination of holomorphic mappings at the boundary Finite jet determination of holomorphic mappings at the boundary

2000-01-21

arxiv.org/abs/math/0001116v2

Mathematics

Complex Variables

27 pages; AMS-TeX; In this revised version, a result showing that smooth CR diffeomorphisms depend smoothly on their jets of a

Scientific paper

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.

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