Chaînes holomorphes de bord donné dans ℂP n
Dolbeault, Pierre ; Henkin, Gennadi
Bulletin de la Société Mathématique de France, Tome 125 (1997), p. 383-445 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{BSMF_1997__125_3_383_0,
     author = {Dolbeault, Pierre and Henkin, Gennadi M.},
     title = {Cha\^\i nes holomorphes de bord donn\'e dans $\mathbb {C}P^n$},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     volume = {125},
     year = {1997},
     pages = {383-445},
     doi = {10.24033/bsmf.2312},
     mrnumber = {98m:32014},
     zbl = {0942.32007},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/BSMF_1997__125_3_383_0}
}

Dolbeault, Pierre; Henkin, Gennadi. Chaînes holomorphes de bord donné dans $\mathbb {C}P^n$. Bulletin de la Société Mathématique de France, Tome 125 (1997) pp. 383-445. doi : 10.24033/bsmf.2312. http://gdmltest.u-ga.fr/item/BSMF_1997__125_3_383_0/

[1]Audin (M.), Lafontaine (J.) ed. - Holomorphic curves in Symplectic Geometry, Progress in Math., Birkhäuser, t. 117, 1994. | MR 95i:58005 | Zbl 0802.53001

[2]Bishop (E.). - Conditions for the analyticity of certain sets, Michigan Math. J., t. 11, 1964, p. 289-304. | MR 29 #6057 | Zbl 0143.30302

[3]Bochner (S.), Martin (W.T.). - Several complex variables, Princeton Math. Ser., t. 10, 1948. | MR 10,366a | Zbl 0041.05205

[4]Chirka (E.M.). - Complex analytic sets, Mathematics and its applications, 46. - Kluwer Academic Publishers, 1989; Russian edition 1985. | Zbl 0683.32002

[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. | MR 97e:32007 | Zbl 0865.32007

[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. | MR 85i:32013 | Zbl 0538.32014

[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. | MR 96a:32020 | Zbl 0821.32008

[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. | MR 80a:32014 | Zbl 0423.32013

[13]Gromov (M.). - Pseudo-holomorphic curves in symplectic manifolds, Inv. math., t. 82, 1985, p. 307-347. | MR 87j:53053 | Zbl 0592.53025

[14]Harvey (R.). - Holomorphic chains and their boundaries, Proc. Symp. Pure Math., t. 30, vol. 1, 1977, p. 309-382. | MR 56 #5929 | Zbl 0374.32002

[15]Harvey (R.), Lawson (B.). - On boundaries of complex analytic varieties, I, Ann. of Math., t. 102, 1975, p. 233-290. | MR 54 #13130 | Zbl 0317.32017

[16]Harvey (R.), Lawson (B.). - On boundaries of complex analytic varieties, II, Ann. of Math., t. 106, 1977, p. 213-238. | MR 58 #17186 | Zbl 0361.32010

[17]Harvey (R.), Lawson (B.). - Complex analytic geometry and measure theory, Proc. Symp. Pure Math., t. 44, 1986, p. 261-274. | MR 87h:32021 | Zbl 0587.32019

[18]Harvey (R.), Shiffman (B.). - A characterization of holomorphic chains, Ann. of Math. (2), t. 99, 1974, p. 553-587. | MR 50 #7572 | Zbl 0287.32008

[19]Henkin (G.), Leiterer (J.). - Andreotti-Grauert theory by integral formulas, Progress in Math., Birkhaüser, Boston, t. 74, 1988. | MR 90h:32002b | Zbl 0654.32002

[20]Henkin (G.), Tumanov (A.E.). - Local characterization of holomorphic automorphisms of Siegel domains, Funct. Anal. and Appl., t. 17, 1983, p. 285-294. | MR 86a:32063 | Zbl 0572.32018

[21]Hörmander (L.). - L2 estimates and existence theorems for the ∂-operator, Acta Math., t. 113, 1965, p. 89-152. | Zbl 0158.11002

[22]Ivashkovich (S.M.). - The Hartogs-type extension theorem for meromorphic maps into compact Kähler manifolds, Inv. Math., t. 109, 1992, p. 47-54. | MR 93g:32016 | Zbl 0782.32009

[23]Jöricke (B.). - Some remarks concerning holomorphically convex hulls and envelopes of holomorphy, Math. Z., t. 218, 1995, p. 143-157. | MR 96b:32014 | Zbl 0816.32011

[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. | MR 31 #1399 | Zbl 0166.33802

[26]Koppelman (W.). - The Cauchy integral for functions of several complex variables, Bull. A.M.S., t. 73, 1967, p. 372-377. | MR 35 #416 | Zbl 0177.11103

[27]Lawrence (M.G.). - Polynomial hulls of rectifiable curves, Amer. J. Math., t. 117, 1995, p. 405-417. | MR 96d:32012 | Zbl 0827.32012

[28]Lelong (P.). - Fonctions entières (n variables) et fonctions plurisousharmoniques d'ordre fini dans ℂn, J. Analyse Math., t. 12, 1964, p. 365-407. | MR 29 #3668 | Zbl 0126.29602

[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. | Numdam | MR 23 #A3281 | Zbl 0199.41203

[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. | MR 18,473b | Zbl 0074.06204

[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. | MR 39 #5830 | Zbl 0184.31401

[33]Rothstein (W.). - Bemerkung zur theorie komplexen Raüme, Math. Ann., t. 137, 1959, p. 304-315. | MR 22 #4081 | Zbl 0088.05704

[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. | Zbl 0145.31803

[35]Sacks (J.), Uhlenbeck (K.). - The existence of minimal 2-spheres, Ann. of Math., t. 113, 1981, p. 1-24. | MR 82f:58035 | Zbl 0462.58014

[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. | MR 37 #464 | Zbl 0165.40503

[38]Stoll (W.). - Über die Fortsetzbarkeit analytischer Mengen endlichen Oberflächeninhaltes, Arch. Math., t. 9, 1958, p. 167-175. | MR 21 #729 | Zbl 0083.30801

[39]Stout (E.L.). - The boundary values of holomorphic functions of several complex variables, Duke Math. J., t. 44, 1977, p. 105-108. | MR 55 #10722 | Zbl 0351.32015

[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. | MR 87f:32035 | Zbl 0586.32016

[41]Wermer (J.). - The hull of a curve in ℂn, Ann. of Math., t. 68, 1958, p. 550-561. | MR 20 #6536 | Zbl 0084.33402

[42]Wu (H.-H.). - The equidistribution theory of holomorphic curves, Ann. of Math. Studies, Princeton Univ. Press, t. 64, 1970. | MR 42 #7951 | Zbl 0199.40901