Finite jet determination of CR mappings

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dc.creatorLamel, Bernhard
dc.creatorMir, Nordine
dc.date2007-06-21
dc.date.accessioned2026-07-07T08:29:46Z
dc.date.available2026-07-07T08:29:46Z
dc.descriptionWe prove the following finite jet determination result for CR mappings: Given a smooth generic submanifold M of C^N, N >= 2, which is essentially finite and of finite type at each of its points, for every point p on M there exists an integer l(p), depending upper-semicontinuously on p, such that for every smooth generic submanifold M' of C^N of the same dimension as M, if h_1 and h_2: (M,p)->M' are two germs of smooth finite CR mappings with the same l(p) jet at p, then necessarily their k-jets agree for all positive integers k. In the hypersurface case, this result provides several new unique jet determination properties for holomorphic mappings at the boundary in the real-analytic case; in particular, it provides the finite jet determination of arbitrary real-analytic CR mappings between real-analytic hypersurfaces in C^N of D'Angelo finite type. It also yields a new boundary version of H. Cartan's uniqueness theorem: if Omega and Omega' are two bounded domains in C^N with smooth real-analytic boundary, then there exists an integer k, depending only on the boundary of Omega, such that if H_1 and H_2: Omega -> Omega' are two proper holomorphic mappings extending smoothly up to the boundary of Omega near some point boundary point p and agreeing up to order k at p, then necessarily H_1=H_2.
dc.descriptionArticle in press at Adv. Math
dc.identifierhttps://arxiv.org/abs/0706.3115
dc.identifierhttp://arxiv.org/abs/0706.3115
dc.identifierAdv. Math., 216(1), (2007), 153--177.
dc.identifierdoi:10.1016/j.aim.2007.05.007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138058
dc.subjectComplex Variables
dc.subject32H02, 32H12, 32V05, 32V15, 32V20, 32V25, 32V35, 32V40
dc.titleFinite jet determination of CR mappings
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