Skip to main content

Boundary Behavior of Holomorphic Mappings

  • Chapter
Several Complex Variables

Abstract

Suppose that f: D1 → D2 is a proper holomorphic mapping between smooth bounded domains D1 and D2 contained in ℂn. There are two fundamental problems in the theory of functions of several complex variables concerning the boundary behavior of f.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Bell and H. Boas, Regularity of the Bergman projection in weakly pseudoconvex domains, Math. Ann. 257 (1981), 23–30.

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Bell, Biholomorphic mappings and the \( \bar \partial \)-problem, Ann. of Math. 114 (1981), 103–113.

    Article  MathSciNet  MATH  Google Scholar 

  4. —, Analytic hypoellipticity of the \( \bar \partial \)-Neumann problem and extendability of holomorphic mappings, Acta Math. 147 (1981), 109–116.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Derridj and D. Tartakoff, On the global real analyticity of solutions to the \( \bar \partial \)-Neumann problem, Comm. Partial Diff. Eqns. 1 (1976), 401–435.

    Article  MathSciNet  MATH  Google Scholar 

  6. K. Diederich and J. E. Fornaess, Pseudoconvex domains with real analytic boundary, Ann. of Math. 107 (1978), 371–384.

    Article  MathSciNet  MATH  Google Scholar 

  7. K. Diederich and J. E. Fornaess, A remark on a paper of S. R. Belly, Manuscripta Math. 34 (1981), 31–44.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds, I and II, Ann. of Math. 78 (1963), 112–148 and 79 (1964), 450–472.

    Article  MathSciNet  Google Scholar 

  10. —, Subellipticity of the \( \bar \partial \)-Neumann problem on pseudoconvex domains: sufficient conditions, Acta Math. 142 (1979), 79–122.

    Article  MathSciNet  MATH  Google Scholar 

  11. G. Komatsu, Global analytic hypoellipticity of the \( \bar \partial \)-Neumann problem, Tôhoku Math. J. Ser. 2, 28 (1976), 145–156.

    Article  MathSciNet  Google Scholar 

  12. D. Tartakoff, The local real analyticity of solutions to b and the \( \bar \partial \)-Neumann problem, Acta Math. 145 (1980), 177–204.

    Article  MathSciNet  MATH  Google Scholar 

  13. F. Trèves, Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications to the \( \bar \partial \)-Neumann problem, Comm. Partial Diff. Eqns. 3 (1978), 475–642.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Birkhäuser Boston, Inc.

About this chapter

Cite this chapter

Bell, S.R. (1984). Boundary Behavior of Holomorphic Mappings. In: Kohn, J.J., Remmert, R., Lu, QK., Siu, YT. (eds) Several Complex Variables. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5296-2_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-5296-2_1

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3189-5

  • Online ISBN: 978-1-4612-5296-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics