Potential Analysis

, 29:409 | Cite as

Pluripolar Hulls and Complete Pluripolar Sets

  • Nguyen Quang DieuEmail author
  • Pham Hoang Hiep


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.


Pluripolar set Complete pluripolar set Pluripolar hull 

Mathematics Subject Classifications (2000)

32U30 30C85 31C10 32D15 


  1. 1.
    Bedford, E., Taylor, A.: A new capacity of plurisubharmonic functions. Acta Math. 149, 1–40 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bedford, E., Taylor, A.: Plurisubharmonic functions with logarithmic singularities. Ann. Inst. Fourier 38, 133–171 (1988)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Cegrell, U.: The general definition of the complex Monge-Ampère operator. Ann. Inst. Fourier 54(1), 159–179 (2004)MathSciNetGoogle Scholar
  4. 4.
    Coltoiu, M.: Complete locally pluripolar sets. J. Reine Angew. Math. 412, 108–112 (1990)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Duval, J., Sibony, N.: Polynomial convexity, rational convexity and currents. Duke Math. J. 79(2), 487–513 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Edlund, T.: Complete pluripolar curves and graphs. Ann. Polon. Math. 84(1), 75–86 (2004)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    El Mir, H.: Sur le prolongement des courants positifs fermés. Acta Math. 153(1–2), 1–45 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 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)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 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)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Klimek, M.: Pluripotential Theory. Oxford Science, Oxford (1991)zbMATHGoogle Scholar
  11. 11.
    Mau Hai, L., Dieu N.Q., Van Long, T.: Remarks on pluripolar hulls. Ann. Polon. Math. 86, 225–236 (2004)Google Scholar
  12. 12.
    Levenberg, N., Poletsky, E.: Pluripolar hulls. Michigan Math. J. 46, 151–162 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Ransford, T.: Potential Theory in the Complex Plane. Cambridge University Press, Cambridge (1995)zbMATHGoogle Scholar
  14. 14.
    Sibony, N.: Quelques problems de prolongement de courants en analyse complexe. Duke Math. J. 52(1), 157–197 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Wiegerinck, J.: The pluripolar hull of {w = e  − 1/z}. Ark. Mat. 38, 201–208 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Wiegerinck, J.: Graphs of holomorphic functions with isolated singularities are complete pluripolar. Mich. Math. J. 47, 191–197 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Zeriahi, A.: Ensembles pluripolaires exceptionels pour la croissance partielle des fonctions holomorphes. Ann. Polon. Math. 50, 81–89 (1989)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsHanoi University of Education (Dai Hoc Su Pham Hanoi)HanoiVietnam

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