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Envelopes of Holomorphy of Domains in Cn

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Book cover Complex Analysis

Part of the book series: Aspects of Mathematics ((ASMA,volume 1))

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Abstract

This note is a survey on results and open problems in the theory of envelopes of holomorphy of domains in Cn.

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References

  1. B. Aimer, Sur quelques problèmes de la théorie des fonctions analytiques de deux variables complexes, Arkiv för Mat. Astron, och Fysik 17 (1922), 1–70.

    Google Scholar 

  2. Th. J. Barth, The Kobayashi indicatrix at the center of a circular domain, Proc. Amer. Math. Soc. 88 (1983), 527–530.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Bedford, Local and global envelopes of holomorphy of domains in C2, Trans. Amer. Math. Soc. 292 (1985), 665–674.

    MathSciNet  MATH  Google Scholar 

  4. E. Bedford, Locally determined envelopes of holomorphy in C2, Math. Ann. 281 (1988), 419–429.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Bochner, A theorem on analytic continuation of functions in several variables, Ann. Math. 39 (1938), 14–19.

    Article  MathSciNet  Google Scholar 

  6. R. Carmignani, Envelopes of holomorphy and holomorphic convexity, Trans. Amer. Math. Soc. 179 (1973), 415–431.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Cartan, Les fonctions de deux variables complexes et le problème de la représentation analytique, J. Math. Pures Appl. (9) 10 (1931), 1–114.

    MathSciNet  Google Scholar 

  8. —, in “Séminaire Cartan,” École Normale Supérieure, 1951/52.

    Google Scholar 

  9. E. Casadio Tarabusi, On holomorphic retractions of domains in Stein manifolds, Istit. Lombardo Accad. Sci. Lett. Rend. A 122 (1988), 285–289.

    MathSciNet  MATH  Google Scholar 

  10. E. Casadio Tarabusi, S. Trapani, Envelopes of holomorphy of Hartogs and circular domains, Pacific J. Math, (to appear).

    Google Scholar 

  11. —, Construction of envelopes of holomorphy for some classes of special domains, (to appear).

    Google Scholar 

  12. K. Diederich, J.-E. Fornæss, A strange bounded smooth domain of holomorphy, Bull. Amer. Math. Soc. 82 (1976), 74–76.

    Article  MathSciNet  MATH  Google Scholar 

  13. J.-E. Fornaess, W. R. Zame, Riemann domains and envelopes of holomorphy, Duke Math. J. 50 (1983), 273–283.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Kajiwara, On the envelope of holomorphy of a generalized tube in Cn, Kōdai Math. Sem. Rep. 15 (1963), 106–110.

    Article  MathSciNet  MATH  Google Scholar 

  15. H. Kerner, Überlagerungen und Holomorphiehüllen, Math. Ann. 144 (1961), 126–134.

    Article  MathSciNet  MATH  Google Scholar 

  16. T. Mokri, “Variétés tubulaires de type H ∞°,” Thèse de 3e cycle, Université de Lille-Flandres-Artois, May 1986.

    Google Scholar 

  17. H. Rossi, On envelops of holomorphy, Comm. Pure Appl. Math. 16 (1963), 9–17.

    Article  MathSciNet  MATH  Google Scholar 

  18. H. L. Royden, One-dimensional cohomology of domains of holomorphy, Ann. Math. 78 (1963), 197–200.

    Article  MathSciNet  MATH  Google Scholar 

  19. Ch. Sacré, Enveloppe d’holomorphie d’un domaine tube de Cm × Cn à fibres connexes, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), 311–314.

    MATH  Google Scholar 

  20. B. Stensønes, “Envelopes of Holomorphy,” Ph.D. Thesis, Princeton University, 1985.

    Google Scholar 

  21. B. Stensønes, Stein neighborhoods, Math. Z. 195 (1987), 433–436.

    Article  MathSciNet  Google Scholar 

  22. B. Stensønes, Envelopes of holomorphy and related questions, Proceedings of the A.M.S. Conference on Complex Analysis, Santa Cruz 1989.

    Google Scholar 

  23. P. Thullen, Zur Theorie der Singularitäten der Funktionen zweier komplexen Veränderlichen (Die Regularitätshüllen), Math. Ann. 106 (1932), 64–76.

    Article  MathSciNet  Google Scholar 

  24. S. Trapani, Complex retractions and envelopes of holomorphy, Proc. Amer. Math. Soc. 104 (1988), 145–148.

    Article  MathSciNet  MATH  Google Scholar 

  25. V. S. Vladimirov, “Methods of the Theory of Functions of Many Complex Variables,” M.I.T. Press, Cambridge, 1966.

    Google Scholar 

  26. V. S. Vladimirov, Analytic functions of several complex variables and quantum field theory, in “Mathematical Problems of Quantum Field Theory and Quantum Statistics, Part I: Axiomatic Quantum Field Theory,” V. S. Vladimirov editor, Proc. Steklov Inst. Math., vol. 1978, no. 1, American Mathematical Society, Providence, 1978, pp. 69–81.

    Google Scholar 

  27. V. S. Vladimirov, M. Shirinbekov, On the construction of envelopes of holomorphy for Hartogs domains (Russian), Ukrain. Mat. Zh. 15 (1963), 189–192; abstract #3175, MR 28 (1964), p. 620.

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, I-38050, Povo (Trento), Italy

    Enrico Casadio Tarabusi

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via Fontanile di Carcaricola, I-00133, Roma, Italy

    Stefano Trapani

Authors
  1. Enrico Casadio Tarabusi
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  2. Stefano Trapani
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik, Bergische Universität Gesamthochschule Wuppertal, Germany

    Klas Diederich

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© 1991 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig

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Tarabusi, E.C., Trapani, S. (1991). Envelopes of Holomorphy of Domains in Cn . In: Diederich, K. (eds) Complex Analysis. Aspects of Mathematics, vol 1. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86856-5_12

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  • DOI: https://doi.org/10.1007/978-3-322-86856-5_12

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-322-86858-9

  • Online ISBN: 978-3-322-86856-5

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