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Strongly pseudoconvex manifolds

  • Modern Methods and New Results in Complex Analysis
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Bibliography

  1. Andreotti, A., and Grauert, H., “Théorémes de finitude pour la cohomologie des espaces complexes,” Bull. Soc. Math. France 90 (1962), 193–259.

    MathSciNet  MATH  Google Scholar 

  2. Andreotti, A., “Théorémes dé dependance algébrique sur les espaces complexes pseudo-concaves,” Bull. Soc. Math. France 91 (1963), 1–38.

    MathSciNet  MATH  Google Scholar 

  3. Bremermann, H. J., Űber die Äquivalenz der pseudo-konvexen Gebiete und der Holomorphie-gebiete im Raum von n komplexen Veränderlichen,” Math. Ann. 128 (1954), 63–91.

    Article  MathSciNet  MATH  Google Scholar 

  4. Bremermann, H. J., “Complex convexity”, Trans. Amer. Math. Soc. 82 (1956) 17–51.

    Article  MathSciNet  MATH  Google Scholar 

  5. Cartan, H., Séminaire E.N.S., 1951–1952, École Normale Supérieure, Paris.

    Google Scholar 

  6. Docquier, F., and Grauert, H., “Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten,” Math. Ann., 140 (1960), 94–123.

    Article  MathSciNet  MATH  Google Scholar 

  7. Garabedian, P. R., and Spencer, D. C., “Complex boundary value problems,” Trans. Amer. Math. Soc. 73 (1952), 223–242.

    Article  MathSciNet  MATH  Google Scholar 

  8. Grauert, H., “On Levi's Problem and the imbedding of real-analytic manifolds,” Ann. Math. 68 (1958), 460–472.

    Article  MathSciNet  MATH  Google Scholar 

  9. Grauert, H., “Űber Modifikationen und exzeptionelle analytische Mengen,” Math. Ann. 146 (1962), 331–368.

    Article  MathSciNet  MATH  Google Scholar 

  10. Grauert, H., und Remmert, R., “Plurisubharmonische Funktionen in Komplexen Räumen,” Math. Zeit., 65 (1956), 175–194.

    Article  MathSciNet  MATH  Google Scholar 

  11. Hironaka, H., “The resolution of singularities of an algebraic variety (characteristic zero),” Ann. Math. 79 (1964), 109–800.

    Article  MathSciNet  MATH  Google Scholar 

  12. Gunning, R. C. and Rossi, H., Analytic Functions of Several Complex Variables, Prentice-Hall, 1965.

    Google Scholar 

  13. Hironaka, H., A Fundamental lemma on point modifications, Conference on Complex Analysis, Minneapolis, Springer-Verlag 1965.

    Google Scholar 

  14. Hörmander, L., L2 estimates and existence theorems for the -operator, Acta Math. 113, 89–152 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  15. Hörmander, L., An Introduction to Complex Analysis in Several Variables, Van Nostrand, 1966.

    Google Scholar 

  16. Hurewicz and Wallman, Dimension theory.

    Google Scholar 

  17. Kohn, J. J., “Harmonic integrals on strongly pseudoconvex manifolds, I., II,” Ann. Math. 78 (1963), 112–148.

    Article  MathSciNet  MATH  Google Scholar 

  18. Kohn, J. J. and Nirenberg, L., Non-coercive boundary problems, Comm. Pure and Appl. Math., 18, 443–492 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  19. Kohn, J. J., and Rossi, H., “On the extension of holomorphic functions from the boundary of a complex manifold” (not published).

    Google Scholar 

  20. Kohn, J. J., and Spencer, D. C., “Complex Neumann problems,” Ann. Math. 66 (1957), 89–140.

    Article  MathSciNet  MATH  Google Scholar 

  21. Kohn, J. J., Boundaries of complex manifolds, Conference on Complex Analysis, Minneapolis, Springer-Verlag 1965.

    Google Scholar 

  22. Lelong, P., “La convexité et les fonctions analytiques de plusieur variables complexes,” J. Math. Pures Appl., 31 (1952)., 191–219.

    MathSciNet  MATH  Google Scholar 

  23. Lelong, P., “Domaines convexes par rapport aux fonctions plurisousharmoniques”, J. d'Analyse Math., 2 (1952–53), 178–208.

    Article  MathSciNet  Google Scholar 

  24. Levi, E. E., “Studii sui punti singolari essenziali delle funzioni analitiche di due o più variabili complesse, “Annali di Mat. pura ed appl. 17, 3 (1910), 61–87.

    Article  MATH  Google Scholar 

  25. Morrey, C. B., “The analytic imbedding of abstract real-analytic manifolds”, Ann. Math. 68 (1958), 159–201.

    Article  MathSciNet  MATH  Google Scholar 

  26. Nagata, M., Local Rings, Interscience 1962.

    Google Scholar 

  27. Narasimhan, R., “The Levi problem for complex spaces,” Math. Ann. 142 (1961), 355–365.

    Article  MathSciNet  MATH  Google Scholar 

  28. Narasimhan, R., “Levi Problem for Complex Spaces II,” Math. Ann. 146 (1962), 195–216.

    Article  MathSciNet  MATH  Google Scholar 

  29. Nirenberg, R., and Wells, R. O., “Holomorphic approximation on real submanifolds of complex manifolds, Bull. A.M.S., 73, 378–381 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  30. Norguet F., “Sur les domaines d'holomorphie des fonctions uniformes de plusieurs variables complexes (passage du local au global),” Bull. Soc. Math. France, 82 (1954), 137–159.

    MathSciNet  MATH  Google Scholar 

  31. Oka, K., Sur les fonctions analytiques de plusieurs variables (Tokyo, Iwanami Shoten, 1961). [This is a collection of reprints of nine articles under the same general title, which have appeared in the following journals: I “Domaines convexes par rapport aux fonctions rationelles,” J. Sci. Hiroshima Univ., ser. A 6 (1936), 245–255. II “Domaines d'holomorphie,” J. Sci. Hiroshima Univ., ser. A 7 (1937), 115–130. III “Deuxième/problème de Cousin,” J. Sci. Hiroshima Univ., ser. A 9 (1939), 7–19. IV “Domaines d'holomorphie et domaines rationellement convexes,” Jap. J. Math. 17 (1941), 517–521. V “L'intégrale de Cauchy,” Jap. J. Math. 17 (1941), 523–531. VI “Domaines pseudoconvexes,” Tohoku Math. J. 49 (1942), 15–52. VII “Sur quelques notions artithmétiques,” Bull. Soc. Math. France 78 (1950), 1–27. VIII “Memme fondamental,” J. Math. Soc. Japan 3 (1951), 204–214 and 259–278. IX “Domaines finis sans point critique intérieur,” Jap. J. Math. 23 (1953), 97–155. Since then, the following paper in the series has also appeared: X “Une mode nouvelle engendrant les domaines pseudoconvexes,” Jap. J. Math. 32 (1962), 1–12.

    MATH  Google Scholar 

  32. Rossi, H., Attaching analytic spaces to an analytic space along a pseudoconcave boundary, Conference on Complex Analysis, Minneapolis, Springer-Verlag, 1965.

    Google Scholar 

  33. Rossi, H., Lecture notes, Seminaires des Mathematiques Supérieures, Montréal, 1967.

    Google Scholar 

  34. Hironaka, H. and Rossi, H., On the equivalence of embeddings of exceptional complex spaces, Math. Annalen, 1965.

    Google Scholar 

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C. T. Taam

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© 1969 Springer-Verlag

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Rossi, H. (1969). Strongly pseudoconvex manifolds. In: Taam, C.T. (eds) Lectures in Modern Analysis and Applications I. Lecture Notes in Mathematics, vol 103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099982

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  • DOI: https://doi.org/10.1007/BFb0099982

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  • Print ISBN: 978-3-540-04622-6

  • Online ISBN: 978-3-540-36145-9

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