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1998 | 70 | 1 | 131-143
Tytuł artykułu

Complex Plateau problem in non-Kähler manifolds

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the complex Plateau problem for strongly pseudoconvex contours in non-Kähler manifolds. We give a necessary and sufficient condition for the existence of solution in the class of manifolds carrying pluriclosed metric forms and propose a conjecture for the general case.
Rocznik
Tom
70
Numer
1
Strony
131-143
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-12-20
poprawiono
1998-04-19
Twórcy
  • Université de Lille-I, U.F.R. de Mathématiques, 59655 Villeneuve d'Ascq Cedex, France
Bibliografia
  • [Ba] D. Barlet, Espace analytique réduit des cycles analytiques complexes compacts d'un espace analytique complexe de dimension finie in: Séminaire Norguet IX, Lecture Notes in Math. 482, Springer, 1975, 1-158.
  • [Db] P. Dolbeault, Geometric measure theory and the calculus of variations in: Proc. Sympos. Pure Math. 44, Amer. Math. Soc., 1986, 171-205.
  • [Db-H] P. Dolbeault et G. Henkin, Surfaces de Riemann de bord donné dans $ℂ ℙ^n$ in: Contributions to Complex Analysis and Analytic Geometry, H. Skoda et al. (eds.), Aspects of Math. E26, Vieweg, 1994, 163-187.
  • [Ga] P. Gauduchon, Les métriques standard d'une surface à premier nombre de Betti pair Astérisque 126 (1985), 129-135.
  • [H] R. Harvey, Holomorphic chains and their boundaries in: Proc. Sympos. Pure Math. 30, Part 1, Amer. Math. Soc., 1977, 307-382.
  • [H-L] R. Harvey and H. Lawson, An intrinsic characterization of Kähler manifolds Invent. Math. 74 (1983), 169-198.
  • [H-L] G. Henkin and J. Leiterer, Theory of Functions on Complex Manifolds Monographs in Math., Birkhäuser, 1984.
  • [Iv-1] S. Ivashkovich, The Hartogs-type extension theorem for the meromorphic maps into compact Kähler manifolds Invent. Math. 109 (1992), 47-54.
  • [Iv-2] S. Ivashkovich, Continuity principle and extension properties of meromorphic mappings with values in non Kähler manifolds MSRI Preprint No. 1997-033, xxx.math-archive: math.CV/9704219.
  • [Iv-3] S. Ivashkovich, One example in concern with extension and separate analyticity properties of meromorphic mappings xxx.math-archive: math.CV/9804009, to appear in Amer. J. Math.
  • [Ka-1] M. Kato, Examples on an extension problem of holomorphic maps and holomorphic 1-dimensional foliations Tokyo J. Math. 13 (1990), 139-146.
  • [Ka-2] M. Kato, Compact quotient manifolds of domains in a complex 3-dimensional projective space and the Lebesgue measure of limit sets ibid. 19 (1996), 99-119.
  • [Ka-3] M. Kato, Compact complex manifolds containing 'global' spherical shells I in: Proc. Internat. Sympos. Algebraic Geometry, Kyoto, 1977, 45-84.
  • [Kl] M. Klimek, Pluripotential Theory London Math. Soc. Monographs (N.S.) 6, Cambridge Univ. Press, 1991.
  • [Lg] P. Lelong, Plurisubharmonic Functions and Positive Differential Forms Gordon and Breach, New York, 1969.
  • [Lv] E. Levi, Studii sui punti singolari essenziali delle funzioni analitiche di due o più variabili complesse Ann. Mat. Pura Appl. 17 (1910), 61-87.
  • [Re] R. Remmert, Holomorphe und meromorphe Abbildungen komplexer Räume Math. Ann. 133 (1957), 328-370.
  • [Rs] H. Rossi, Attaching analytic spaces to an analytic space along a pseudoconvex boundary in: Proc. Conf. Complex Analysis (Minneapolis, 1964), Springer, 1965, 242-256.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv70z1p131bwm
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