Skip to main content

Extension Problems and Positive Currents in Complex Analysis

  • Chapter
Contributions to Several Complex Variables

Summary

This paper is a survey of recent developments in the theory of the extension of analytic sets and closed, positive currents.

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.

Bibliographie

  1. H.ALEXANDER. Continuing 1dimensional analytic sets. Math. Annalen, 191, 1970, p. 14.

    Google Scholar 

  2. J. BECKER. Continuing analytic sets across IRn. Math. Annalen, 195, 1972, 103–106.

    Article  Google Scholar 

  3. E. BEDFORD and B. A. TAYLOR. A new capacity for plurisubharmonic functions. Acta Math., 149, 1982, 1–39.

    Article  MathSciNet  MATH  Google Scholar 

  4. E. BISHOP. Conditions for the analyticity of certain sets. Michigan Math. Jour., 11, 1964, p. 289–304.

    Article  MATH  Google Scholar 

  5. J.P.DEMAILLY. Courants positifs extrémaux et conjecture de Hodge. Inventiones Mathematicae, 69, 1982, 347–374.

    Article  MathSciNet  MATH  Google Scholar 

  6. J.P.DEMAILLY. Propagation des singularités des courants, positifs, fermés. Arkiv für Mathematik, 1983.

    Google Scholar 

  7. K. DIEDERICH and J.E. FORNAESS. Smooth but not complexanalytic pluripolar sets. Manuscripta Mathematica, 37, 1982, p. 121–125.

    Article  MathSciNet  MATH  Google Scholar 

  8. H.EL MIR. Sur le prolongement des courants,positifs,fermés. Thèse d’Etat sou tenue à l’Université de Paris VI en Novembre 1982.

    Google Scholar 

  9. H.EL MIR. Sur le prolongement des courants,positifs,fermés. Acta Mathematica, 153, 1984, p. 1–45.

    Article  MathSciNet  MATH  Google Scholar 

  10. H.FEDERER. Geometric Measure Theory. Springer Berlin, Heidelberg, NewYork, 1969.

    MATH  Google Scholar 

  11. P.GRIFFITHS. Two theorems on extension of holomorphic mappings. Inventiones Math., 14, 1971, 27–62.

    Article  MATH  Google Scholar 

  12. R. HARVEY. Removable singularities for positive currents. Amer. Jour. of Math., 96, 1974, 67–68.

    Article  MathSciNet  MATH  Google Scholar 

  13. R.HARVEY. Holomorphic chains and their boundaries. Proceeding of Symposia in Pure Mathematics. Several complex variables, Williamstown, 1975, Vol. 30, 1977, 309–382.

    Article  MathSciNet  Google Scholar 

  14. R. HARVEY and J. R.KING. On the structure of positive currents. Invent. Math. 15, 1972, p. 47–52.

    Article  MathSciNet  MATH  Google Scholar 

  15. R. HARVEY and J. POLKING. Extending analytic objects. Comm. pure and applied Math., 28, 1975, 701–727.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. KING. The currents defined by analytic varieties. Acta Math. 127, 1971, p. 185–220.

    Article  MathSciNet  MATH  Google Scholar 

  17. P.LELONG. Intégration sur un ensemble analytique complexe. Bull. Soc. Math. France, 85, 1957, p. 239–262.

    MathSciNet  MATH  Google Scholar 

  18. P.LELONG. Fonctions entières ( n variables) et fonctions plurisousharmoniques d’ordre fini dans Iç. Jour. Anal. Math. Jérusalem, 12, 1964, p. 365–407.

    MathSciNet  MATH  Google Scholar 

  19. P.LELONG., Fonctions plurisousharmoniques et formes différentielles positives. Gordon and Breach, Dunod, Paris, Londres, NewYork, 1968.

    MATH  Google Scholar 

  20. B.SHIFFMAN. On the continuation of analytic sets. Math. Ann. 185, 1970, 1–12.

    Article  MathSciNet  MATH  Google Scholar 

  21. N.SIBONY. Quelques problèmes de prolongement de courants en analyse complexe. Préprint Université d’Orsay, 1984, à paraître au Duke Math. Jour.,1984.

    Google Scholar 

  22. Y.T. SIU. Analyticity of Sets associated to Lelong Numbers and the extension of closed positive currents. Inventiones Math., 27, 1974, p. 53–156.

    Article  MathSciNet  MATH  Google Scholar 

  23. H.SIU. Extension of meromorphic maps into Kahler manifolds. Annals of Mathematics, 102, 1975, 421–462.

    Article  MathSciNet  MATH  Google Scholar 

  24. H.SKODA. Prolongement des courants, positifs, fermés, de masse finie, Inventiones Mathematicae, 66, 1982, p. 361–376.

    Article  MathSciNet  MATH  Google Scholar 

  25. W.STOLL. Uber die Fortsetzbarkeit analytischer Mengen endlichen Oberflächeninhaltes. Archiv der Mathematik, 9, 1958, 167–175.

    Article  MathSciNet  MATH  Google Scholar 

  26. W.STOLL. The growth of the area of a transcendental analytic set I and II. Math. Annalen, t. 156, 1964, p. 47–48 et 144–170.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer Fachmedien Wiesbaden

About this chapter

Cite this chapter

Skoda, H. (1986). Extension Problems and Positive Currents in Complex Analysis. In: Howard, A., Wong, PM. (eds) Contributions to Several Complex Variables. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-06816-7_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-663-06816-7_14

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-08964-1

  • Online ISBN: 978-3-663-06816-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics