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Pluripolar Hulls and Complete Pluripolar Sets

Abstract

We study the pluripolar hull of a complex subvariety in the complement of a closed complete pluripolar set. A result on propagation of pluripolar hulls is also given.

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References

  1. Bedford, E., Taylor, A.: A new capacity of plurisubharmonic functions. Acta Math. 149, 1–40 (1982)

    MATH  Article  MathSciNet  Google Scholar 

  2. Bedford, E., Taylor, A.: Plurisubharmonic functions with logarithmic singularities. Ann. Inst. Fourier 38, 133–171 (1988)

    MATH  MathSciNet  Google Scholar 

  3. Cegrell, U.: The general definition of the complex Monge-Ampère operator. Ann. Inst. Fourier 54(1), 159–179 (2004)

    MathSciNet  Google Scholar 

  4. Coltoiu, M.: Complete locally pluripolar sets. J. Reine Angew. Math. 412, 108–112 (1990)

    MATH  MathSciNet  Google Scholar 

  5. Duval, J., Sibony, N.: Polynomial convexity, rational convexity and currents. Duke Math. J. 79(2), 487–513 (1995)

    MATH  Article  MathSciNet  Google Scholar 

  6. Edlund, T.: Complete pluripolar curves and graphs. Ann. Polon. Math. 84(1), 75–86 (2004)

    MATH  MathSciNet  Article  Google Scholar 

  7. El Mir, H.: Sur le prolongement des courants positifs fermés. Acta Math. 153(1–2), 1–45 (1984)

    MATH  Article  MathSciNet  Google Scholar 

  8. Edigarian, A., Wiegerinck, J.: The pluripolar hull of the graph of a holomorphic function with polar singularities. Indiana Math. J. 52(6), 1663–1680 (2003)

    MATH  Article  MathSciNet  Google Scholar 

  9. Edigarian, A., Wiegerinck, J.: Determination of the pluripolar hulls of graphs of certain holomorphic functions. Ann. Inst. Fourier (Grenoble) 54(6), 2085–2104 (2004)

    MATH  MathSciNet  Google Scholar 

  10. Klimek, M.: Pluripotential Theory. Oxford Science, Oxford (1991)

    MATH  Google Scholar 

  11. Mau Hai, L., Dieu N.Q., Van Long, T.: Remarks on pluripolar hulls. Ann. Polon. Math. 86, 225–236 (2004)

    Google Scholar 

  12. Levenberg, N., Poletsky, E.: Pluripolar hulls. Michigan Math. J. 46, 151–162 (1999)

    MATH  Article  MathSciNet  Google Scholar 

  13. Ransford, T.: Potential Theory in the Complex Plane. Cambridge University Press, Cambridge (1995)

    MATH  Google Scholar 

  14. Sibony, N.: Quelques problems de prolongement de courants en analyse complexe. Duke Math. J. 52(1), 157–197 (1985)

    MATH  Article  MathSciNet  Google Scholar 

  15. Wiegerinck, J.: The pluripolar hull of {w = e  − 1/z}. Ark. Mat. 38, 201–208 (2000)

    MATH  Article  MathSciNet  Google Scholar 

  16. Wiegerinck, J.: Graphs of holomorphic functions with isolated singularities are complete pluripolar. Mich. Math. J. 47, 191–197 (2000)

    MATH  Article  MathSciNet  Google Scholar 

  17. Zeriahi, A.: Ensembles pluripolaires exceptionels pour la croissance partielle des fonctions holomorphes. Ann. Polon. Math. 50, 81–89 (1989)

    MATH  MathSciNet  Google Scholar 

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Correspondence to Nguyen Quang Dieu.

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Dieu, N.Q., Hiep, P.H. Pluripolar Hulls and Complete Pluripolar Sets. Potential Anal 29, 409 (2008). https://doi.org/10.1007/s11118-008-9103-7

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  • DOI: https://doi.org/10.1007/s11118-008-9103-7

Keywords

  • Pluripolar set
  • Complete pluripolar set
  • Pluripolar hull

Mathematics Subject Classifications (2000)

  • 32U30
  • 30C85
  • 31C10
  • 32D15