On the local meromorphic extension of CR meromorphic mappings

Joël Merker; Egmont Porten

Annales Polonici Mathematici, Tome 69 (1998), p. 163-193 / Harvested from The Polish Digital Mathematics Library

Résumé

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) $f :_{f} \to Y$ 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 $ℂ^{m + n} \times Y$ 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.

Publié le : 1998-01-01

Zbl 0927.32024

EUDML-ID : urn:eudml:doc:262638

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     author = {Jo\"el Merker and Egmont Porten},
     title = {On the local meromorphic extension of CR meromorphic mappings},
     journal = {Annales Polonici Mathematici},
     volume = {69},
     year = {1998},
     pages = {163-193},
     zbl = {0927.32024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv70z1p163bwm}
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Joël Merker; Egmont Porten. On the local meromorphic extension of CR meromorphic mappings. Annales Polonici Mathematici, Tome 69 (1998) pp. 163-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv70z1p163bwm/

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