Skip to main content
SpringerLink
Log in

On the Hausdorff property of some Dolbeault cohomology groups

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Cassa, A.: Coomologia separata sulle varietà analitiche complesse. Ann. Scuola Norm. Sup. Pisa 25, 291–323 (1971)

    MathSciNet  MATH  Google Scholar 

  2. Chakrabarti, D., Shaw, M.-C.: \(L^2\) Serre duality on domains in complex manifolds and applications. Trans. Am. Math. Soc. 364, 3529–3554 (2012)

    Article  MathSciNet  Google Scholar 

  3. Chaumat, J., Chollet, A.-M.: Régularité höldérienne de l’opérateur \(\overline{\partial }\) sur le triangle de Hartogs. Ann. Inst. Fourier 41, 867–882 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, S.-C., Shaw, M.-C.: Partial differential equations in several complex variables. Studies in Advanced Mathematics, vol. 19. AMS-International Press, Brooklyn (2001)

  5. Dufresnoy, A.: Sur l’opérateur \(d^{\prime \prime }\) et les fonctions différentiables au sens de Whitney. Ann. Inst. Fourier (Grenoble) 29(1), xvi, 229–238 (1979)

    Google Scholar 

  6. Folland, G.B., Kohn, J.J.: The Neumann problem for the Cauchy–Riemann complex. Annals of Mathematics Studies, vol. 75. Princeton University Press, Princeton; University of Tokyo Press, Tokyo (1972)

  7. Fu, S.: Hearing pseudoconvexity with the Kohn Laplacian. Math. Ann. 331, 475–485 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hörmander, L.: The null space of the \({\bar{\partial }}\)-Neumann operator. Ann. Inst. Fourier (Grenoble) 54, 1305–1369 (2004)

    Article  MathSciNet  Google Scholar 

  9. Kohn, J.J.: Global regularity for \(\bar{\partial }\) on weakly pseudoconvex manifolds. Trans. Am. Math. Soc. 181, 273–292 (1973)

    MathSciNet  MATH  Google Scholar 

  10. Laufer, H.B.: On Serre duality and envelopes of holomorphy. Trans. Am. Math. Soc. 128, 414–436 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  11. Laufer, H.B.: On the infinite dimensionality of the Dolbeault cohomology groups. Proc. Am. Math. Soc. 52, 293–296 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  12. Laurent-Thiébaut, C., Leiterer, J.: On Serre duality. Bull. Sci. Math. 124, 93–106 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Serre, J.P.: Un théorème de dualité. Comment. Math. Helv. 29, 9–26 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  14. Shaw, M.-C.: The closed range property for on domains with pseudoconcave boundary. In: Proceedings for the Fribourg conference, Trends in Mathematics, pp. 307–320 (2010)

  15. Shaw, M.-C.: Duality between harmonic and Bergman spaces. Geometric analysis of several complex variables and related topics, Contemporary Mathematics, vol. 550, pp. 161–171. American Mathematical Society, Providence (2011)

  16. Trapani, S.: Inviluppi di olomorfia et gruppi di coomologia di Hausdorff. Rend. Sem. Mat. Univ. Padova 75, 25–37 (1986)

    MathSciNet  MATH  Google Scholar 

  17. Trapani, S.: Coomologia di Hausdorff e forma di Levi. Ann. Mat. Pura Appl. 144, 391–401 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  18. Trapani, S.: Holomorphically convex compact sets and cohomology. Pac. J. Math. 134, 179–196 (1988)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Dr. Debraj Chakrabarti for his comments and suggestions on the first version of this paper. They would also like to thank Professor Stefano Trapani for pointing out some of his earlier work related to this paper (see [16–18] in the references).

Author information

Authors and Affiliations

  1. Institut Fourier, UJF-Grenoble 1, 38041 , Grenoble, France

    Christine Laurent-Thiébaut

  2. Institut Fourier, CNRS UMR 5582, 38402 , Saint-Martin d’Hères, France

    Christine Laurent-Thiébaut

  3. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Mei-Chi Shaw

Authors
  1. Christine Laurent-Thiébaut
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mei-Chi Shaw
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christine Laurent-Thiébaut.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Laurent-Thiébaut, C., Shaw, MC. On the Hausdorff property of some Dolbeault cohomology groups. Math. Z. 274, 1165–1176 (2013). https://doi.org/10.1007/s00209-012-1111-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-012-1111-z

Keywords

Mathematics Subject Classification (2000)

Search

Navigation