ArticleOriginal scientific text

Title

Phénomène de Hartogs-Bochner dans les variétés CR

Authors 1

Affiliations

  1. Université de Grenoble I, Institut Fourier, Laboratoire de Mathématiques associé au CNRS (URA 188), B.P. 74, 38402 Saint-Martin-d'Hères Cedex, France

Bibliography

  1. [Ai/He] R. A. Airapetjan and G. M. Henkin, Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions, Russian Math. Surveys 39 (1984), 41-118.
  2. [An/G] A. Andreotti et H. Grauert, Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193-259.
  3. [An/Hi] A. Andreotti and C. D. Hill, E. E. Levi convexity and the Hans Lewy problem. Part I: Reduction to vanishing theorems, Ann. Scuola Norm. Sup. Pisa 26 (1972), 325-363.
  4. [Ba] M. Y. Barkatou, Estimation höldérienne d'un noyau local de type Martinelli-Bochner sur les hypersurfaces 1-convexes-concaves, Applications, Math. Z., à paraître.
  5. [Bo] S. Bochner, Analytic and meromorphic continuation by means of Green's formula, Ann. of Math. 44 (1943), 652-673.
  6. [Či] E. M. Čirka, Analytic representation of CR functions, Math. USSR-Sb. 27 (1975), 526-553.
  7. [Eh] L. Ehrenpreis, A new proof and an extension of Hartogs theorem, Bull. Amer. Math. Soc. 67 (1961), 507-509.
  8. [Fi/Le] B. Fischer and J. Leiterer, A local Martinelli-Bochner formula on hypersurfaces, Math. Z. 214 (1993), 659-681.
  9. [Fi/Li] W. Fischer und I. Lieb, Lokale Kerne und beschränkte Lösungen für den ∂̅-Operator auf q-konvexen Gebieten, Math. Ann. 208 (1974), 249-265.
  10. [Ha/La] R. Harvey and H. B. Lawson, Boundaries of complex analytic varieties I, Ann. of Math. 102 (1975), 233-290.
  11. [He 1] G. M. Henkin, Solution des équations de Cauchy-Riemann tangentielles sur des variétés de Cauchy-Riemann q-convexes, C. R. Acad. Sci. Paris Sér. I Math.292 (1981), 27-30.
  12. [He 2] G. M. Henkin, The Hartogs-Bochner effect on CR manifolds, Soviet Math. Dokl. 29 (1984), 78-82.
  13. [He 3] G. M. Henkin, The method of integral representations in complex analysis, in: Sovremennye problemy matematiki, Fundamental'nye napravleniya 7, Moscow, VINITI, 1985, 23-124 (in Russian); English transl.: Encyclopedia of Math. Sci. 7, Several Complex Variables I, Springer, 1990, 19-116.
  14. [He/Le] G. M. Henkin and J. Leiterer, Andreotti-Grauert Theory by Integral Formulas, Birkhäuser, 1988.
  15. [Ky] A. M. Kytmanov, Holomorphic extension of CR-functions with singularities on a hypersurface, Math. USSR-Izv. 37 (1991), 681-691.
  16. [L-T] C. Laurent-Thiebaut, Sur l'extension des fonctions CR dans une variété de Stein, Ann. Mat. Pura Appl. 150 (1988), 141-152.
  17. [L-T 1] C. Laurent-Thiebaut, Résolution du ̅b à support compact et phénomène de Hartogs-Bochner dans les variétés CR, in: Proc. Sympos. Pure Math. 52 (1991), 239-249.
  18. [L-T 2] C. Laurent-Thiebaut, Phénomène de Hartogs-Bochner relatif dans une hypersurface réelle 2-concave d'une variété analytique complexe, Math. Z. 212 (1993), 511-525.
  19. [L-T/L] C. Laurent-Thiebaut and J. Leiterer, On the Hartogs-Bochner extension phenomenon for differential forms, Math. Ann. 284 (1989), 103-119.
  20. [Lu] G. Lupacciolu, A theorem on holomorphic extension of CR functions, Pacific J. Math. 124 (1986), 177-191.
  21. [Lu 1] G. Lupacciolu, Some global results on extension of CR objects in complex manifolds, Trans. Amer. Math. Soc. 321 (1990), 761-774.
  22. [Lu 2] G. Lupacciolu, Characterization of removable sets in strongly pseudo-convex boundaries, à paraître.
  23. [Lu/To] G. Lupacciolu et G. Tomassini, Un teorema di estensione per le CR-funzioni, Ann. Mat. Pura Appl. 137 (1984), 257-263.
  24. [Ma 1] E. Martinelli, Sopra una dimonstrazione di R. Fueter per un teorema di Hartogs, Comment. Math. Helv. 15 (1943), 340-349.
  25. [Ma 2] E. Martinelli, Sulla determinazione di una funzione analitica più variabili complesse in un campo, assegnatone la traccia sulla frontiera, Ann. Mat. Pura Appl. 55 (1961), 192-202.
  26. [N] I. Naruki, Localization principle for differential complexes and its applications, Publ. Res. Inst. Math. Sci. Kyoto Univ. 8 (1972), 43-110.
  27. [St] E. L. Stout, Removable singularities for the boundary values of holomorphic functions, in: Math. Notes 38, Princeton University Press, 1993, 600-629.
Pages:
233-247
Main language of publication
French
Published
1995
Exact and natural sciences