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1998 | 70 | 1 | 163-193
Tytuł artykułu

On the local meromorphic extension of CR meromorphic mappings

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $(f,𝓓_f,[Γ_f])$, where: 1) $f: 𝓓_f → Y$ is a 𝓒¹-smooth mapping defined over a dense open subset $𝓓_f$ 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 𝓒¹-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 $(f,𝓓_f,[Γ_f])$ extends meromorphically to a wedge attached to M if M is everywhere minimal and $𝓒^ω$ (real-analytic) or if M is a $𝓒^{2,α}$ globally minimal hypersurface.
Rocznik
Tom
70
Numer
1
Strony
163-193
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-12-20
poprawiono
1998-09-04
Twórcy
autor
  • Laboratoire d'Analyse, Topologie et Probabilités, UMR 6632, Centre de Mathématiques et d'Informatique, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France
  • Max-Planck-Gesellschaft, Humboldt-Universität zu Berlin, Jägerstrasse, 10-11, D-10117 Berlin, Germany
Bibliografia
  • [1] E. Chirka, Complex Analytic Sets, Kluwer, Dordrecht, 1989.
  • [2] E. M. Chirka and E. L. Stout, Removable singularities in the boundary, in: Contributions to Complex Analysis and Analytic Geometry, Aspects of Math. E26, Vieweg, 1994, 43-104.
  • [3] T.-C. Dinh and F. Sarkis, Wedge removability of metrically thin sets and application to the CR meromorphic extension, preprint, 1997.
  • [4] P. Dolbeault et G. M. Henkin, Chaînes holomorphes de bord donné dans $ℂ ℙ^n$, Bull. Soc. Math. France 125 (1997), 383-446.
  • [5] F. R. Harvey and H. B. Lawson, On boundaries of complex analytic varieties, Ann. of Math., I: 102 (1975), 233-290; II: 106 (1977), 213-238.
  • [6] S. M. Ivashkovich, The Hartogs-type extension theorem for meromorphic maps into compact Kähler manifolds, Invent. Math. 109 (1992), 47-54.
  • [7] B. Jöricke, Removable singularities for CR-functions, Ark. Mat. 26 (1988), 117-143.
  • [8] B. Jöricke, Envelopes of holomorphy and CR-invariant subsets of CR-manifolds, C. R. Acad. Sci. Paris Sér. I 315 (1992), 407-411.
  • [9] B. Jöricke, Deformation of CR- manifolds, minimal points and CR-manifolds with the microlocal analytic extension property, J. Geom. Anal. 6 (1996), 555-611.
  • [10] B. Jöricke, Some remarks concerning holomorphically convex hulls and envelope of holomorphy, Math. Z. 218 (1995), 143-157.
  • [11] B. Jöricke, Boundaries of singularity sets, removable singularities, and CR-invariant subsets of CR-manifolds, preprint, 1996.
  • [12] G. Lupacciolu, A theorem on holomorphic extension of CR-functions, Pacific J. Math. 124 (1986), 177-191.
  • [13] C. Laurent-Thiébaut, Sur l'extension de fonctions CR dans une variété de Stein, Ann. Mat. Pura Appl. (4) 150 (1988), 141-151.
  • [14] J. Merker, Global minimality of generic manifolds and holomorphic extendibility of CR functions, Internat. Math. Res. Notices 8 (1994), 329-342.
  • [15] J. Merker, On removable singularities for CR functions in higher codimension, ibid. 1 (1997), 21-56.
  • [16] J. Merker and E. Porten, On removable singularities for integrable CR functions, preprint, 1997; available at: http://www.dmi.ens.fr/EDITION/preprints.
  • [17] E. Porten, thesis, Berlin, 1996.
  • [18] E. Porten, A Hartogs-Bochner type theorem for continuous CR mappings, manuscript, 1997.
  • [19] F. Sarkis, CR meromorphic extension and the non embedding of the Andreotti-Rossi CR structure in the projective space, Internat. J. Math., to appear.
  • [20] B. Shiffman, Separately meromorphic mappings into Kähler manifolds, in: Contributions to Complex Analysis and Analytic Geometry, Aspects of Math. E26, Vieweg, 1994, 243-250.
  • [21] J.-M. Trépreau, Sur la propagation des singularités dans les variétés CR, Bull. Soc. Math. France 118 (1990), 403-450.
  • [22] A. E. Tumanov, Connections and propagation of analyticity for CR functions, Duke Math. J. 73 (1994), 1-24.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv70z1p163bwm
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