Meylan, Francine; Mir, Nordine; Zaitsev, Dmitri 'Approximation and convergence of formal CR-mappings' International Mathematics Research Notes, 2003, (4), 2002 pp 211 - 242
International Mathematics Research Notes 2003 4
Let M ⊂ CN be a minimal real-analytic CR-submanifold and M′ ⊂ CN′
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.
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