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The imbedding problem for open complex manifolds

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1268)

Keywords

  • Finite Type
  • Real Hypersurface
  • Pseudoconvex Domain
  • Bergman Kernel
  • Stein Manifold

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Bibliography

  1. Bedford, E., Bell, S. and Catlin, D., "Boundary behavior of proper holomorphic mappings," Mich. Math. J. 30 (1983), 107–111.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Bell, S., "Biholomorphic mappings and the ∂-problem," Ann. of Math. (2) 114 (1981), 103–133.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Bell, S. and Catlin D., "Boundary regularity of proper holomorphic mappings," Duke Math. J. 49 (1982), 385–396.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Bell, S. and Ligocka, E., "A simplification and extension of Fefferman's theorem on biholomorphic mappings," Invent. Math. 57 (1980), 283–289.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Bishop, E., "Mappings of partially analytic spaces," Amer. J. Math. 83 (1961), 209–242.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Bland, J., "On the existence of bounded holomorphic functions on complete Kähler manifolds," Invent. Math. 81 (1985), 555–566.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Bland, J., "The Einstein-Kähler metric on {|z|2+|w|2p < l}," Mich. Math. J. 33 (1986), 209–220.

    CrossRef  MathSciNet  Google Scholar 

  8. Bland, J., "Bounded imbeddings of open Kähler manifolds in CN," preprint.

    Google Scholar 

  9. Bloom, T., and Graham, I., "A geometric characterization of points of type m on real hypersurfaces," J. Diff. Geom. 12 (1977), 171–182.

    MathSciNet  MATH  Google Scholar 

  10. Boutet de Monvel, L., "Integration des equations de Cauchy-Riemann induites formelles," Seminaire Goulaouic-Schwartz, 1974–75.

    Google Scholar 

  11. Burns, D., Diederich, K., and Schnider, S., "Distinguished curves in pseudoconvex boundaries," Duke Math. J. 44 (1977), 407–431.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Catlin, D., "Necessary conditions for subellipticity of the ∂-Neumann problem," Ann. of Math. 117 (1983), 147–171.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. _____, "Boundary invariants of pseudoconvex domains," Ann. of Math. 120 (1984), 529–586.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. _____, "Global regularity of the ∂-Neumann problem," Proc. Sym. Pure Math., vol. 41, Amer. Math. Soc., Providence, R.I. (1984), 39–49.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. _____, "Subelliptic estimates for the ∂-Neumann problem on pseudoconvex domains," preprint.

    Google Scholar 

  16. Cheng, S.Y., and Yau, S.-T., "On the existence of a Kähler metric on noncompact complex manifolds and the regularity of Fefferman's equations," Comm. Pure Appl. Math. 33 (1980), 507–544.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Chern, S.S. and Moser, J.K., "Real hypersurfaces in complex manifolds," Acta Math. 133 (1974), 219–271.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. D'Angelo, J., "Real hypersurfaces, orders of contact, and applications," Ann. of Math. (2) 115 (1982), 615–637.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. _____, "Finite type conditions for real hypersurfaces in Cn," preprint.

    Google Scholar 

  20. Diederich, K., and Fornaess, J.E., "Boundary regularity of proper holomorphic mappings," Invent. Math. 67 (1982), 363–384.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Fefferman, C., "The Bergman kernel and biholomorphic mappings of pseudoconvex domains," Invent. Math. 26 (1974), 1–65.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. Fefferman, C., "Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains," Ann. of Math. 103 (1976), 395–416.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. Folland, G.B. and Kohn, J.J., "The Neumann problem for the Cauchy-Riemann complex," Ann. of Math. Studies, no. 75, Princeton Univ. Press, Princeton, N.J., 1972.

    MATH  Google Scholar 

  24. Fornaess, J.E., "Biholomorphic mappings between weakly pseudoconvex domains," Pacific J. Math. 74 (1978), 63–65.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. Greene, R.E. and Wu, H., "Curvature and complex analysis. I, II, III," Bull. Amer. Math. Soc. 77 (1971) 1045–1049; ibid. 78 (1972), 866–870; 79 (1973), 606–608.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. _____, "On the subharmonicity and plurisubharmonicity of geodesically convex functions," Indiana Univ. Math. J. 22 (1973), 641–653.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. _____, "Some function-theoretic properties of noncompact Kähler manifolds," Proc. Sym. Pure Math., vol. 27, part II, Amer. Math. Soc., Providence, R.I. (1975), 33–41.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. _____, "C convex functions and manifolds of positive curvature," Acta Math. 137 (1976), 209–245.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. _____, "Analysis on noncompact Kähler manifolds," Proc. Sym. Pure Math., vol. 30, part II, Providence, R.I. (1977), 69–100.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. _____, "Gap theorems for noncompact Riemannian manifolds," Duke Math. J. 49 (1982), 731–756.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  33. Hörmander, L., "An introduction to complex analysis in several variables," Van Nostrand, Princeton, N.J. 1966.

    MATH  Google Scholar 

  34. Klembeck, P., "Kähler metrics of negative curvature, the Bergman metric near the boundary and the Kobayashi metric on smooth bounded strictly pseudoconvex sets," Indiana Math. J. 27 (2) (1978), 275–282.

    CrossRef  MathSciNet  MATH  Google Scholar 

  35. Kohn, J.J., "Harmonic integrals on strongly pseudoconvex manifolds, I, II", Ann. of Math. (2) 78 (1963), 112–148; ibid. (2) 79 (1964), 450–472.

    CrossRef  MathSciNet  MATH  Google Scholar 

  36. _____, "Boundary behaviour of ∂ on weakly pseudoconvex manifolds of dimension two," J. Diff. Geom. 6 (1972), 523–542.

    MathSciNet  MATH  Google Scholar 

  37. _____, "Global regularity for ∂ on weakly pseudoconvex manifolds," Trans. Amer. Math. Soc. 181 (1973), 273–292.

    MathSciNet  MATH  Google Scholar 

  38. _____, "Methods of partial differential equations," Proc. Sym. Pure Math., vol. 30, Part I, Amer. Math. Soc., Providence, R.I. (1977), 215–237.

    CrossRef  MathSciNet  Google Scholar 

  39. _____, "Subellipticity of the ∂-Neumann problem on pseudoconvex domains: Sufficient conditions," Acta Math. 142 (1979), 79–122.

    CrossRef  MathSciNet  MATH  Google Scholar 

  40. Kohn, J.J. and Nirenberg, L., "Noncoercive boundary value problems," Comm. Pure Appl. Math. 18 (1965), 443–492.

    CrossRef  MathSciNet  MATH  Google Scholar 

  41. Lempert, L., "La métrique de Kobayashi et la répresentation des domaine sur la boule," Bull. Soc. Math. France 109 (1981), 427–474.

    MathSciNet  MATH  Google Scholar 

  42. Mok, N., Siu, Y.T. and Yau, S.-T., "The Poincaré-Lelong equation on complete Kähler manifolds," Compositio Math. 44 (1981), no. 1–3, 183–218.

    MathSciNet  MATH  Google Scholar 

  43. Mok, N. and Yau, S.-T., "Completeness of the Kähler Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions," Proc. Sym. Pure Math., Vol. 39, Part I, Providence, R.I. (1983), 41–59.

    CrossRef  MathSciNet  MATH  Google Scholar 

  44. Narasimhan, R., "Imbedding of holomorphically complete complex spaces," Amer. J. Math. 82 (1960), 917–934.

    CrossRef  MathSciNet  MATH  Google Scholar 

  45. Remmert, R., "Sur les espaces analytiques holomorphiquement séparables et holomorphiquement convexes," C.R. Acad. Sci. Paris 243 (1956), 118–121.

    MathSciNet  MATH  Google Scholar 

  46. Rossi, H. and Taylor J., "On algebras of holomorphic functions on finite pseudoconvex manifolds," J. Functional Anal. 24 (1977), 11–31.

    CrossRef  MathSciNet  MATH  Google Scholar 

  47. Siu, Y.T., and Yau, S.-T., "Complete Kähler manifolds with nonpositive curvature of faster than quadratic decay," Ann. of Math. 105 (1977), 225–264.

    CrossRef  MathSciNet  MATH  Google Scholar 

  48. Webster, S., "Kähler metrics associated to a real hypersurface," Comment. Math. Helvetici 52 (1977), 235–250.

    CrossRef  MathSciNet  MATH  Google Scholar 

  49. Yau, S.-T., "Harmonic Functions on complete Riemannian manifolds," Comm. Pure Appl. Math. 28 (1975), 201–228.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1987 Springer-Verlag

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Bland, J.S. (1987). The imbedding problem for open complex manifolds. In: Krantz, S.G. (eds) Complex Analysis. Lecture Notes in Mathematics, vol 1268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097295

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  • DOI: https://doi.org/10.1007/BFb0097295

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  • Print ISBN: 978-3-540-18094-4

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