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Please use this identifier to cite or link to this item: http://hdl.handle.net/2262/31981

Title: Approximation and convergence of formal CR-mappings
Author: ZAITSEV, DMITRI
Author's Homepage: http://people.tcd.ie/zaitsevd
Keywords: Pure & Applied Mathematics
Issue Date: 2003
Publisher: Oxford University Press
Citation: Meylan, Francine; Mir, Nordine; Zaitsev, Dmitri 'Approximation and convergence of formal CR-mappings' International Mathematics Research Notes, 2003, (4), 2002 pp 211 - 242
Series/Report no.: International Mathematics Research Notes
2003
4
Abstract: Let M ⊂ CN be a minimal real-analytic CR-submanifold and M′ ⊂ CN′ a realalgebraic subset through points p ∈ M and p′ ∈ M′. We show that that any formal (holomorphic) mapping f : (CN, p) → (CN′ , p′), sending M into M′, can be approximated up to any given order at p by a convergent map sending M into M′. If M is furthermore generic, we also show that any such map f, that is not convergent, must send (in an appropriate sense) M into the set E′ ⊂ M′ of points of D’Angelo infinite type. Therefore, if M′ does not contain any nontrivial complex-analytic subvariety through p′, any formal map f as above is necessarily convergent.
Description: PUBLISHED
URI: http://dx.doi.org/10.1155/S1073792803205146
http://hdl.handle.net/2262/31981
Appears in Collections:Pure & Applied Mathematics (Scholarly Publications)

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