On the local meromorphic extension of CR meromorphic mappings

Joël Merker; Egmont Porten

Annales Polonici Mathematici (1998)

  • Volume: 70, Issue: 1, page 163-193
  • ISSN: 0066-2216

Abstract

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Let M be a generic CR submanifold in ℂ m + n , m = CR dim M ≥ 1, n = codim M ≥ 1, d = dim M = 2m + n. A CR meromorphic mapping (in the sense of Harvey-Lawson) is a triple ( f , f , [ Γ f ] ) , where: 1) f : f → Y is a ¹-smooth mapping defined over a dense open subset f of M with values in a projective manifold Y; 2) the closure Γ f of its graph in ℂ m + n × Y defines an oriented scarred ¹-smooth CR manifold of CR dimension m (i.e. CR outside a closed thin set) and 3) d [ Γ f ] = 0 in the sense of currents. We prove that ( f , f , [ Γ f ] ) extends meromorphically to a wedge attached to M if M is everywhere minimal and ω (real-analytic) or if M is a 2 , α globally minimal hypersurface.

How to cite

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Joël Merker, and Egmont Porten. "On the local meromorphic extension of CR meromorphic mappings." Annales Polonici Mathematici 70.1 (1998): 163-193. <http://eudml.org/doc/262638>.

@article{JoëlMerker1998,
abstract = {Let M be a generic CR submanifold in $ℂ^\{m+n\}$, m = CR dim M ≥ 1, n = codim M ≥ 1, d = dim M = 2m + n. A CR meromorphic mapping (in the sense of Harvey-Lawson) is a triple $(f,_f,[Γ_f])$, where: 1) $f: _f → Y$ is a ¹-smooth mapping defined over a dense open subset $_f$ of M with values in a projective manifold Y; 2) the closure $Γ_f$ of its graph in $ℂ^\{m+n\} × Y$ defines an oriented scarred ¹-smooth CR manifold of CR dimension m (i.e. CR outside a closed thin set) and 3) $d[Γ_f] = 0$ in the sense of currents. We prove that $(f,_f,[Γ_f])$ extends meromorphically to a wedge attached to M if M is everywhere minimal and $^ω$ (real-analytic) or if M is a $^\{2,α\}$ globally minimal hypersurface.},
author = {Joël Merker, Egmont Porten},
journal = {Annales Polonici Mathematici},
keywords = {CR generic currents; scarred CR manifolds; removable singularities for CR functions; deformations of analytic discs; CR meromorphic mappings},
language = {eng},
number = {1},
pages = {163-193},
title = {On the local meromorphic extension of CR meromorphic mappings},
url = {http://eudml.org/doc/262638},
volume = {70},
year = {1998},
}

TY - JOUR
AU - Joël Merker
AU - Egmont Porten
TI - On the local meromorphic extension of CR meromorphic mappings
JO - Annales Polonici Mathematici
PY - 1998
VL - 70
IS - 1
SP - 163
EP - 193
AB - Let M be a generic CR submanifold in $ℂ^{m+n}$, m = CR dim M ≥ 1, n = codim M ≥ 1, d = dim M = 2m + n. A CR meromorphic mapping (in the sense of Harvey-Lawson) is a triple $(f,_f,[Γ_f])$, where: 1) $f: _f → Y$ is a ¹-smooth mapping defined over a dense open subset $_f$ of M with values in a projective manifold Y; 2) the closure $Γ_f$ of its graph in $ℂ^{m+n} × Y$ defines an oriented scarred ¹-smooth CR manifold of CR dimension m (i.e. CR outside a closed thin set) and 3) $d[Γ_f] = 0$ in the sense of currents. We prove that $(f,_f,[Γ_f])$ extends meromorphically to a wedge attached to M if M is everywhere minimal and $^ω$ (real-analytic) or if M is a $^{2,α}$ globally minimal hypersurface.
LA - eng
KW - CR generic currents; scarred CR manifolds; removable singularities for CR functions; deformations of analytic discs; CR meromorphic mappings
UR - http://eudml.org/doc/262638
ER -

References

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