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Compactness of families of holomorphic mappings up to the boundary

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

Keywords

  • Compact Subset
  • Finite Type
  • Real Hypersurface
  • Pseudoconvex Domain
  • Bergman Kernel

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References

  1. D.E. Barrett, Regularity of the Bergman projection on domains with transverse symmetries, Math. Ann. 258 (1982), 441–446.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. E. Bedford, Proper holomorphic mappings from domains with real analytic boundary, Amer. J. Math. 106 (1984), 745–760.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. E. Bedford, Action of the automorphisms of a smooth domain in C n, Proc. A.M.S. 93 (1985), 232–234.

    MathSciNet  MATH  Google Scholar 

  4. S. Bell, Non-vanishing of the Bergman kernel function at boundary points of certain domains in C n, Math. Ann. 244 (1979), 69–74.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. S. Bell, Boundary behavior of proper holomorphic mappings between non-pseudoconvex domains, Amer. J. Math. 106 (1984), 639–643.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. S. Bell, Differentiability of the Bergman kernel and pseudo-local estimates, Math. Zeit., in press.

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. H. P. Boas, Extension of Kerzman's theorem on differentiability of the Bergman kernel function, to appear.

    Google Scholar 

  10. H. P. Boas, Counterexample to the Lu Qi-Keng conjecture, to appear.

    Google Scholar 

  11. H. Cartan, Sur les fonctions de plusieurs variables complexes: L'itération des transformations intérieurs d'un domaine borné, Math. Zeit. 35 (1932), 760–773.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. D. Catlin, Boundary invariants of pseudoconvex domains, Ann. Math. 120 (1984) 529–586.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. D. Catlin, Subelliptic estimates for the ∂-Neumann problem on pseudoconvex domains, Ann. Math., to appear.

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. R. Greene and S. Krantz, The automorphism groups of strongly pseudoconvex domains, Math. Ann. 261 (1982), 425–446.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. N. Kerzman, The Bergman kernel function. Differentiability at the boundary, Math. Ann. 195 (1972), 149–158.

    CrossRef  MathSciNet  Google Scholar 

  17. R. Narasimhan, Several Complex Variables, Chicago Lectures in Mathematics, University of Chicago Press, 1971.

    Google Scholar 

  18. J.P. Rosay, Sur une caractérisation de la boule parmi les domaines de C n par son groupe d'automorphismes, Ann. Inst. Fourier 29 (4) (1979), 91–97.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1987 Springer-Verlag

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Bell, S. (1987). Compactness of families of holomorphic mappings up to the boundary. In: Krantz, S.G. (eds) Complex Analysis. Lecture Notes in Mathematics, vol 1268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097294

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  • DOI: https://doi.org/10.1007/BFb0097294

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18094-4

  • Online ISBN: 978-3-540-47752-5

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