Skip to main content
Log in

Pseudoconvexité au-dessus d'espaces plus ou moins homogènes

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Bibliographie

  1. Barth, W.: Fortsetzung meromorpher Funktionen in Tori und komplexprojektiver Räumen. Inventiones math.5, 42–62 (1968)

    Google Scholar 

  2. Boutet de Monvel, L., Hirschowitz, A., Pham, F.: Espaces de Hartogs. C.R.A.S.273, 514–516 (1971)

    Google Scholar 

  3. Bremermann, H. J.: Über die Äquivalenz der pseudokonvexen Gebiete und der Holomorphiegebiete im Raum vonn komplexen Veränderlichen. Math. Ann.128, 63–91 (1954)

    Google Scholar 

  4. Cartan, H.: Variétés analytiques complexes et cohomologie. Colloque sur les fonctions de plusieurs variables. Bruxelles 1953

  5. Cartan, H., Thullen, P.: Regularitäts- und Konvergenzbereiche. Math. Ann.106, 617–647 (1932)

    Google Scholar 

  6. Chow, W. L.: On meromorphic maps of algebraic varieties. Annals of Maths.89, 391–403 (1969)

    Google Scholar 

  7. Coddington, E. A., Levinson, N.: Theory of Ordinary Differential Equations. New York: Mac Graw Hill 1955

    Google Scholar 

  8. Dieudonné, J. A.: Elements d'Analyse IV Paris: Gauthier-Villars 1971

    Google Scholar 

  9. Docquier, F., Grauert, H.: Levisches Problem und Rungescher Satz für Tellgebiete Steinscher Mannigfaltigkeiten. Math. Ann.140, 94–123 (1960)

    Google Scholar 

  10. Douady, A.: Espaces sous-algébriques. Séminaire Bourbaki, exposé 344 (1968)

  11. Fujita, R.: Domaines sans point critique intérieur sur l'espace projectif complexe. J. Math. Soc. Japan15, 443–473 (1963)

    Google Scholar 

  12. Fujita, R.: Domaines sans point critique intérieur sur l'espace produit. J. Math. Kyoto Univ.4, 493–514 (1964-1965)

    Google Scholar 

  13. Goto, M.: On algebraic homogeneous spaces. Amer. J. of Math.76, 811–818 (1954)

    Google Scholar 

  14. Grauert, H.: On Levi's problem and the imbedding of real-analytic manifolds. Ann. Math.68, 460–472 (1958)

    Google Scholar 

  15. Grauert, H., Remmert, R.: Konvexität in der komplexen Analysis. Comment. Math. Helv.31, 152–183 (1956)

    Google Scholar 

  16. Griffiths, P. A.: Two theorems on Extensions of Holomorphic Mappings. Inventiones math.14, 27–62 (1971)

    Google Scholar 

  17. Hironaka, H.: Introduction aux ensembles sous-analytiques. Dans: Singularités à Cargèse. Astérisque7–8, 13–20 (1973)

    Google Scholar 

  18. Hironaka, H., Matsumura, H.: Formal functions and formal imbeddings. Preprint

  19. Hirschowitz, A.: Sur la géométric analytique au-dessus des Grassmanniennes. C.R.A.S.271, 1167–1170 (1970)

    Google Scholar 

  20. Hormander, L.: An introduction to Complexe Analysis in Several Variables Princeton: Van Nostrand 1966

    Google Scholar 

  21. Houzel, C.: Géométrie analytique locale I à IV. Séminaire H. Cartan 1960–1961, Paris

  22. Kajiwara, J., Sakai, E.: Generalization of Levi-Oka's Theorem Concerning Meromorphic Functions. Nagoya Math. J.29, 75–84 (1967)

    Google Scholar 

  23. Kaup, W.: Infinitesimale Transformationsgruppen komplexer Räume. Math. Ann.160, 72–92 (1965)

    Google Scholar 

  24. Kiselman, C. O.: On entire functions of exponential type and indicators of analytic functionals. Acta Math.117, 1–35 (1967)

    Google Scholar 

  25. Lelong, P.: Fonctions entiéres de type exponentiel. Université de Montréal. Séminaire 1966

  26. Lelong, P.: Fonctions plurisousharmoniques et formes difféntielles positives, Paris: Gordon & Breach 1968

    Google Scholar 

  27. Levi, E. E.: Studii dui punti singolari essenziali delle funzioni analitiche di due o più variabili complesse. Annali di Math. (3)17, 61–87 (1910)

    Google Scholar 

  28. Malgrange, B.: Lectures on the theory of Functions of Several Complex Variables. Bombay, Tata Inst. of Fund. Res. 1958

  29. Matsugu, Y.: The Levi problem for a product manifold. Pac. J. of Math.46, 231–233 (1973)

    Google Scholar 

  30. Moisezon, B. G.: Onn-dimensional compact complex varieties with algebraically independent meromorphic functions (I. II. III). Amer. Math. Soc. Transl. (2)63, 51–177 (1967)

    Google Scholar 

  31. Narasimhan, R.: The Levi Problem for complex spaces II. Math. Ann.146, 195–215 (1962)

    Google Scholar 

  32. Narasimhan, R.: The Levi Problem in the theory of functions of several complex variables. Proceedings ICM 385-388 (1962)

  33. Nishino, T.: Sur les ensembles pseudoconcaves. J. Math. Kyoto Univ.I, 225–245 (1961–1962)

    Google Scholar 

  34. Norguet, F.: Sur les domaines d'holomorphie des fonctions aniformes de plusieurs variables complexes. Bull. Soc. Math. France82, 137–159 (1954)

    Google Scholar 

  35. Oka, K.: Domaines finis sans point critique intérieur. Japan. J. Math.23, 97–155 (1953)

    Google Scholar 

  36. Remmert, R.: Projektionen analytischer Mengen. Math. Ann.130, 410–441 (1956)

    Google Scholar 

  37. Remmert, R., Van de Ven, A.: Zur Funktionentheorie homogener komplexer Mannigfaltigkeiten. Topology2, 137–157 (1963)

    Google Scholar 

  38. Rothstein, W.: Zur Theorie der Singularitäten analytischer Funktionen und Flächen. Math. Ann.126, 221–238 (1953)

    Google Scholar 

  39. Rossi, H.: Continuation of subvarieties of projective varieties. American J. Math.91, 567–575 (1969)

    Google Scholar 

  40. Schottenloher M.: Über analytische Fortsetzung in Banachräume. Math. Ann.199, 313–336 (1972)

    Google Scholar 

  41. Serre, P.: Représentations linéaires et espaces homogènes kählériens des groupes de Lie compacts. Séminaire Bourbaki exposé no 100 (1954)

  42. Seven, F.: Alcune proprictà fondamentali dell'insieme dei punti singolari di una funzione analitica di più variabili. Mem. R.Accad. Ital.3, (Mat.) N. 1 (1932)

  43. Stein, K.: Überlagerungen holomorph-vollständiger komplexer Räume. Arch. Math.7, 354–361 (1956)

    Google Scholar 

  44. Stein, K.: Einführung in der Funktionentheorie mehrerer Veränderlicher. Vorlesungsausarbeitung München (1962)

  45. Takeuchi, A.: Domaines pseudoconvexes infinis et la métrique riemanienne dans un espace projectif. J. Math. Soc. Japan16, 159–181 (1964)

    Google Scholar 

  46. Tits, J.: Sur certaines classes d'espaces homogenes de groupes de Lie. Mém. Acad. Roy. Belg.29, 168 (1955)

    Google Scholar 

  47. Wang, H. C.: Closed manifolds with homogeneous complex structure. Amer. J. of Math.76, 1–32 (1954)

    Google Scholar 

  48. Warner, G.: Harmonic Analysis on semi-simple Lie Groups 1 Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

A la mémoire d'André Martineau

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hirschowitz, A. Pseudoconvexité au-dessus d'espaces plus ou moins homogènes. Invent Math 26, 303–322 (1974). https://doi.org/10.1007/BF01425555

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01425555

Navigation