Chaînes holomorphes de bord donné dans
Pierre Dolbeault; Gennadi Henkin
Bulletin de la Société Mathématique de France (1997)
- Volume: 125, Issue: 3, page 383-445
- ISSN: 0037-9484
Access Full Article
topHow to cite
topDolbeault, 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]AUDIN (M.), LAFONTAINE (J.) ed. — Holomorphic curves in Symplectic Geometry, Progress in Math., Birkhäuser, t. 117, 1994. Zbl0802.53001MR95i:58005
- [2]BISHOP (E.). — Conditions for the analyticity of certain sets, Michigan Math. J., t. 11, 1964, p. 289-304. Zbl0143.30302MR29 #6057
- [3]BOCHNER (S.), MARTIN (W.T.). — Several complex variables, Princeton Math. Ser., t. 10, 1948. Zbl0041.05205MR10,366a
- [4]CHIRKA (E.M.). — Complex analytic sets, Mathematics and its applications, 46. — Kluwer Academic Publishers, 1989; Russian edition 1985. Zbl0683.32002
- [5]DARBOUX (L.). — Théorie des surfaces, I, 2e éd. — Gauthier-Villars, Paris, 1914.
- [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]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]DOLBEAULT (P.). — On holomorphic chains with given boundary in ℂPn, Springer Lectures Notes, t. 1089, 1983, p. 118-129. Zbl0538.32014MR85i:32013
- [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]DOLBEAULT (P.), HENKIN (G.). — Chaînes holomorphes de bord donné dans ℂPn, Institut de Mathématiques de Jussieu, prépublication 76, 1996.
- [11]DOLBEAULT (P.), POLY (J.B.). — Variations sur le problème des bords dans ℂPn, prépublication, 1995.
- [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]GROMOV (M.). — Pseudo-holomorphic curves in symplectic manifolds, Inv. math., t. 82, 1985, p. 307-347. Zbl0592.53025MR87j:53053
- [14]HARVEY (R.). — Holomorphic chains and their boundaries, Proc. Symp. Pure Math., t. 30, vol. 1, 1977, p. 309-382. Zbl0374.32002MR56 #5929
- [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]HARVEY (R.), LAWSON (B.). — On boundaries of complex analytic varieties, II, Ann. of Math., t. 106, 1977, p. 213-238. Zbl0361.32010MR58 #17186
- [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]HARVEY (R.), SHIFFMAN (B.). — A characterization of holomorphic chains, Ann. of Math. (2), t. 99, 1974, p. 553-587. Zbl0287.32008MR50 #7572
- [19]HENKIN (G.), LEITERER (J.). — Andreotti-Grauert theory by integral formulas, Progress in Math., Birkhaüser, Boston, t. 74, 1988. Zbl0654.32002MR90h:32002b
- [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]HÖRMANDER (L.). — L2 estimates and existence theorems for the ∂-operator, Acta Math., t. 113, 1965, p. 89-152. Zbl0158.11002
- [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]JÖRICKE (B.). — Some remarks concerning holomorphically convex hulls and envelopes of holomorphy, Math. Z., t. 218, 1995, p. 143-157. Zbl0816.32011MR96b:32014
- [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]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]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]LAWRENCE (M.G.). — Polynomial hulls of rectifiable curves, Amer. J. Math., t. 117, 1995, p. 405-417. Zbl0827.32012MR96d:32012
- [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]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]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]PORTEN (E.). — A Hartogs-type theorem for meromorphic mappings, preprint 1997.
- [32]ROSSI (H.). — Continuation of subvarieties of projective varieties, Amer. J. of Math., t. 91, 1969, p. 565-575. Zbl0184.31401MR39 #5830
- [33]ROTHSTEIN (W.). — Bemerkung zur theorie komplexen Raüme, Math. Ann., t. 137, 1959, p. 304-315. Zbl0088.05704MR22 #4081
- [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]SACKS (J.), UHLENBECK (K.). — The existence of minimal 2-spheres, Ann. of Math., t. 113, 1981, p. 1-24. Zbl0462.58014MR82f:58035
- [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]SHIFFMAN (B.). — On the removal of singularities of analytic sets, Michigan Math. J., t. 15, 1968, p. 111-120. Zbl0165.40503MR37 #464
- [38]STOLL (W.). — Über die Fortsetzbarkeit analytischer Mengen endlichen Oberflächeninhaltes, Arch. Math., t. 9, 1958, p. 167-175. Zbl0083.30801MR21 #729
- [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]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]WERMER (J.). — The hull of a curve in ℂn, Ann. of Math., t. 68, 1958, p. 550-561. Zbl0084.33402MR20 #6536
- [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
top- Tien-Cuong Dinh, Problème du bord dans l'espace projectif complexe
- Tien-Cuong Dinh, Conjecture de Globevnik-Stout et théorème de Morera pour une chaîne holomorphe
- Samuele Mongodi, Alberto Saracco, Non compact boundaries of complex analytic varieties in Hilbert spaces
- Tien-Cuong Dinh, Sur la caractérisation du bord d'une chaîne holomorphe dans l'espace projectif
- Joël Merker, Egmont Porten, On the local meromorphic extension of CR meromorphic mappings
- Andrea Altomani, C. Denson Hill, Mauro Nacinovich, Egmont Porten, Holomorphic extension from weakly pseudoconcave CR manifolds
- Tien-Cuong Dinh, Mark G. Lawrence, Polynomial hulls and positive currents
- Frédéric Sarkis, Problème de Plateau complexe dans les variétés kählériennes
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.