Chaînes holomorphes de bord donné dans P n

Pierre Dolbeault; Gennadi Henkin

Bulletin de la Société Mathématique de France (1997)

  • Volume: 125, Issue: 3, page 383-445
  • ISSN: 0037-9484

How to cite

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Dolbeault, Pierre, and Henkin, Gennadi. "Chaînes holomorphes de bord donné dans $\mathbb {C}P^n$." Bulletin de la Société Mathématique de France 125.3 (1997): 383-445. <http://eudml.org/doc/87770>.

@article{Dolbeault1997,
author = {Dolbeault, Pierre, Henkin, Gennadi},
journal = {Bulletin de la Société Mathématique de France},
keywords = {boundary problem; homolomorphic chains; currents; -concave subspaces},
language = {fre},
number = {3},
pages = {383-445},
publisher = {Société mathématique de France},
title = {Chaînes holomorphes de bord donné dans $\mathbb \{C\}P^n$},
url = {http://eudml.org/doc/87770},
volume = {125},
year = {1997},
}

TY - JOUR
AU - Dolbeault, Pierre
AU - Henkin, Gennadi
TI - Chaînes holomorphes de bord donné dans $\mathbb {C}P^n$
JO - Bulletin de la Société Mathématique de France
PY - 1997
PB - Société mathématique de France
VL - 125
IS - 3
SP - 383
EP - 445
LA - fre
KW - boundary problem; homolomorphic chains; currents; -concave subspaces
UR - http://eudml.org/doc/87770
ER -

References

top
  1. [1]AUDIN (M.), LAFONTAINE (J.) ed. — Holomorphic curves in Symplectic Geometry, Progress in Math., Birkhäuser, t. 117, 1994. Zbl0802.53001MR95i:58005
  2. [2]BISHOP (E.). — Conditions for the analyticity of certain sets, Michigan Math. J., t. 11, 1964, p. 289-304. Zbl0143.30302MR29 #6057
  3. [3]BOCHNER (S.), MARTIN (W.T.). — Several complex variables, Princeton Math. Ser., t. 10, 1948. Zbl0041.05205MR10,366a
  4. [4]CHIRKA (E.M.). — Complex analytic sets, Mathematics and its applications, 46. — Kluwer Academic Publishers, 1989; Russian edition 1985. Zbl0683.32002
  5. [5]DARBOUX (L.). — Théorie des surfaces, I, 2e éd. — Gauthier-Villars, Paris, 1914. 
  6. [6]DINH TIEN CUONG (P.). — Chaînes holomorphes à bord rectifiable, C. R. Acad. Sci. Paris, t. 322, Série I, 1996, p. 1135-1140. Zbl0865.32007MR97e:32007
  7. [7]DINH TIEN CUONG (P.). — Enveloppe polynômiale d'un compact de longueur finie et chaînes holomorphes à bord rectifiable, Institut de Mathématiques de Jussieu, prépublication 93, 1996, à paraître dans Acta Mathematica. 
  8. [8]DOLBEAULT (P.). — On holomorphic chains with given boundary in ℂPn, Springer Lectures Notes, t. 1089, 1983, p. 118-129. Zbl0538.32014MR85i:32013
  9. [9]DOLBEAULT (P.), HENKIN (G.). — Surfaces de Riemann de bord donné dans ℂPn, Contributions to complex analysis and analytic geometry, Aspects of Math., Vieweg, t. 26, 1994, p. 163-187. Zbl0821.32008MR96a:32020
  10. [10]DOLBEAULT (P.), HENKIN (G.). — Chaînes holomorphes de bord donné dans ℂPn, Institut de Mathématiques de Jussieu, prépublication 76, 1996. 
  11. [11]DOLBEAULT (P.), POLY (J.B.). — Variations sur le problème des bords dans ℂPn, prépublication, 1995. 
  12. [12]GINDIKIN (S.), HENKIN (G.). — Integral geometry for ∂-cohomology in q-linear concave domains in ℂPn, Funct. Anal. and Appl., t. 12, 1978, p. 247-261. Zbl0423.32013MR80a:32014
  13. [13]GROMOV (M.). — Pseudo-holomorphic curves in symplectic manifolds, Inv. math., t. 82, 1985, p. 307-347. Zbl0592.53025MR87j:53053
  14. [14]HARVEY (R.). — Holomorphic chains and their boundaries, Proc. Symp. Pure Math., t. 30, vol. 1, 1977, p. 309-382. Zbl0374.32002MR56 #5929
  15. [15]HARVEY (R.), LAWSON (B.). — On boundaries of complex analytic varieties, I, Ann. of Math., t. 102, 1975, p. 233-290. Zbl0317.32017MR54 #13130
  16. [16]HARVEY (R.), LAWSON (B.). — On boundaries of complex analytic varieties, II, Ann. of Math., t. 106, 1977, p. 213-238. Zbl0361.32010MR58 #17186
  17. [17]HARVEY (R.), LAWSON (B.). — Complex analytic geometry and measure theory, Proc. Symp. Pure Math., t. 44, 1986, p. 261-274. Zbl0587.32019MR87h:32021
  18. [18]HARVEY (R.), SHIFFMAN (B.). — A characterization of holomorphic chains, Ann. of Math. (2), t. 99, 1974, p. 553-587. Zbl0287.32008MR50 #7572
  19. [19]HENKIN (G.), LEITERER (J.). — Andreotti-Grauert theory by integral formulas, Progress in Math., Birkhaüser, Boston, t. 74, 1988. Zbl0654.32002MR90h:32002b
  20. [20]HENKIN (G.), TUMANOV (A.E.). — Local characterization of holomorphic automorphisms of Siegel domains, Funct. Anal. and Appl., t. 17, 1983, p. 285-294. Zbl0572.32018MR86a:32063
  21. [21]HÖRMANDER (L.). — L2 estimates and existence theorems for the ∂-operator, Acta Math., t. 113, 1965, p. 89-152. Zbl0158.11002
  22. [22]IVASHKOVICH (S.M.). — The Hartogs-type extension theorem for meromorphic maps into compact Kähler manifolds, Inv. Math., t. 109, 1992, p. 47-54. Zbl0738.32008MR93g:32016
  23. [23]JÖRICKE (B.). — Some remarks concerning holomorphically convex hulls and envelopes of holomorphy, Math. Z., t. 218, 1995, p. 143-157. Zbl0816.32011MR96b:32014
  24. [24]KING (J.). — Open problems in geometric function theory, Proceedings of the fifth international symposium, division of Math., p. 4, The Taniguchi foundation, 1978. 
  25. [25]KOHN (J.J.), ROSSI (H.). — On the extension of holomorphic functions from the boundary of a complex manifold, Ann. of Math., t. 81, 1965, p. 451-472. Zbl0166.33802MR31 #1399
  26. [26]KOPPELMAN (W.). — The Cauchy integral for functions of several complex variables, Bull. A.M.S., t. 73, 1967, p. 372-377. Zbl0177.11103MR35 #416
  27. [27]LAWRENCE (M.G.). — Polynomial hulls of rectifiable curves, Amer. J. Math., t. 117, 1995, p. 405-417. Zbl0827.32012MR96d:32012
  28. [28]LELONG (P.). — Fonctions entières (n variables) et fonctions plurisousharmoniques d'ordre fini dans ℂn, J. Analyse Math., t. 12, 1964, p. 365-407. Zbl0126.29602MR29 #3668
  29. [29]LERAY (J.). — Le calcul différentiel et intégral sur une variété analytique complexe (Problème de Cauchy III), Bull. S.M.F., t. 87, 1959, p. 81-180. Zbl0199.41203MR23 #A3281
  30. [30]LEVY (H.). — On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for functions of two complex variables, Ann. of Math., t. 64, 1956, p. 514-522. Zbl0074.06204MR18,473b
  31. [31]PORTEN (E.). — A Hartogs-type theorem for meromorphic mappings, preprint 1997. 
  32. [32]ROSSI (H.). — Continuation of subvarieties of projective varieties, Amer. J. of Math., t. 91, 1969, p. 565-575. Zbl0184.31401MR39 #5830
  33. [33]ROTHSTEIN (W.). — Bemerkung zur theorie komplexen Raüme, Math. Ann., t. 137, 1959, p. 304-315. Zbl0088.05704MR22 #4081
  34. [34]ROTHSTEIN (W.), SPERLING (H.). — Einsetzer und analytischer Flächenstücke in Zyklen auf komplexer Raüme, Festshrift zur Gedächtnisfeier für Karl Weierstrass 1815-1965 (Behnke und Kopfermann, ed.). Westentsche Verlag, Köln, 1965, p. 531-554. Zbl0145.31803
  35. [35]SACKS (J.), UHLENBECK (K.). — The existence of minimal 2-spheres, Ann. of Math., t. 113, 1981, p. 1-24. Zbl0462.58014MR82f:58035
  36. [36]SARKIS (F.). — CR meromorphic extension and the non embedding of the Andreotti-Rossi CR structure in the projective space, Institut de Mathématiques de Jussieu, prébublication 116, 1997. 
  37. [37]SHIFFMAN (B.). — On the removal of singularities of analytic sets, Michigan Math. J., t. 15, 1968, p. 111-120. Zbl0165.40503MR37 #464
  38. [38]STOLL (W.). — Über die Fortsetzbarkeit analytischer Mengen endlichen Oberflächeninhaltes, Arch. Math., t. 9, 1958, p. 167-175. Zbl0083.30801MR21 #729
  39. [39]STOUT (E.L.). — The boundary values of holomorphic functions of several complex variables, Duke Math. J., t. 44, 1977, p. 105-108. Zbl0351.32015MR55 #10722
  40. [40]TRÉPREAU (J.-M.). — Sur le prolongement holomorphe des fonctions CR définies sur une hypersurface réelle de classe C2 dans ℂ2, Inv. Math., t. 83, 1986, p. 583-592. Zbl0586.32016MR87f:32035
  41. [41]WERMER (J.). — The hull of a curve in ℂn, Ann. of Math., t. 68, 1958, p. 550-561. Zbl0084.33402MR20 #6536
  42. [42]WU (H.-H.). — The equidistribution theory of holomorphic curves, Ann. of Math. Studies, Princeton Univ. Press, t. 64, 1970. Zbl0199.40901MR42 #7951

Citations in EuDML Documents

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  1. Tien-Cuong Dinh, Conjecture de Globevnik-Stout et théorème de Morera pour une chaîne holomorphe
  2. Tien-Cuong Dinh, Problème du bord dans l'espace projectif complexe
  3. Samuele Mongodi, Alberto Saracco, Non compact boundaries of complex analytic varieties in Hilbert spaces
  4. Tien-Cuong Dinh, Sur la caractérisation du bord d'une chaîne holomorphe dans l'espace projectif
  5. Joël Merker, Egmont Porten, On the local meromorphic extension of CR meromorphic mappings
  6. Andrea Altomani, C. Denson Hill, Mauro Nacinovich, Egmont Porten, Holomorphic extension from weakly pseudoconcave CR manifolds
  7. Tien-Cuong Dinh, Mark G. Lawrence, Polynomial hulls and positive currents
  8. Frédéric Sarkis, Problème de Plateau complexe dans les variétés kählériennes

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