Approximation and convergence properties of formal CR-maps Academic Article

abstract

• Let M N be a minimal real-analytic CR-submanifold and M N a real-algebraic subset through points p M and p M respectively. We show that that any formal (holomorphic) mapping f: ( N, p) ( N 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 sending M into M is necessarily convergent. 2002 Acadmie des sciences/ditions scientifiques et mdicales Elsevier SAS.

authors

• Mir, Nordine

published proceedings

• Comptes Rendus Mathmatique

author list (cited authors)

• Meylan, F., Mir, N., & Zaitsev, D.

citation count

• 0

complete list of authors

• Meylan, Francine||Mir, Nordine||Zaitsev, Dmitri

publication date

• October 2002

publisher

• Elsevier  Publisher

published in

• Comptes Rendus Mathematique (Academie des Sciences)  Journal

Digital Object Identifier (DOI)

• 10.1016/s1631-073x(02)02552-9

start page

• 671

end page

• 676

volume

• 335

issue

• 8

URL

• http://dx.doi.org/10.1016/s1631-073x(02)02552-9