Finite jet determination of holomorphic mappings at the boundary

By P. Ebenfelt. 2000

48 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5f40eec847e2b7029ab2a39f9adeaab3c6463775

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Equivalence and embedding problems for CR-structures of any codimension (2001, background): “1”
Reflection Ideals and mappings between generic submanifolds in complex space (2000, background): “In another direction, Ebenfelt [18] obtained results on finite determination (not covered by Theorem 1.”
Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case (2001, methodology): “For other results on finite jet determination and finite jet parametrization of local CR automorphisms (in the finite type case), the reader is referred to the papers [H], [BER2,4], [Ha], [L], [BMR], [ E1 ], [K], [KZ].”