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
Bedford, E., Taylor, A.: A new capacity of plurisubharmonic functions. Acta Math. 149, 1–40 (1982)
Bedford, E., Taylor, A.: Plurisubharmonic functions with logarithmic singularities. Ann. Inst. Fourier 38, 133–171 (1988)
Cegrell, U.: The general definition of the complex Monge-Ampère operator. Ann. Inst. Fourier 54(1), 159–179 (2004)
Coltoiu, M.: Complete locally pluripolar sets. J. Reine Angew. Math. 412, 108–112 (1990)
Duval, J., Sibony, N.: Polynomial convexity, rational convexity and currents. Duke Math. J. 79(2), 487–513 (1995)
Edlund, T.: Complete pluripolar curves and graphs. Ann. Polon. Math. 84(1), 75–86 (2004)
El Mir, H.: Sur le prolongement des courants positifs fermés. Acta Math. 153(1–2), 1–45 (1984)
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)
Edigarian, A., Wiegerinck, J.: Determination of the pluripolar hulls of graphs of certain holomorphic functions. Ann. Inst. Fourier (Grenoble) 54(6), 2085–2104 (2004)
Klimek, M.: Pluripotential Theory. Oxford Science, Oxford (1991)
Mau Hai, L., Dieu N.Q., Van Long, T.: Remarks on pluripolar hulls. Ann. Polon. Math. 86, 225–236 (2004)
Levenberg, N., Poletsky, E.: Pluripolar hulls. Michigan Math. J. 46, 151–162 (1999)
Ransford, T.: Potential Theory in the Complex Plane. Cambridge University Press, Cambridge (1995)
Sibony, N.: Quelques problems de prolongement de courants en analyse complexe. Duke Math. J. 52(1), 157–197 (1985)
Wiegerinck, J.: The pluripolar hull of {w = e − 1/z}. Ark. Mat. 38, 201–208 (2000)
Wiegerinck, J.: Graphs of holomorphic functions with isolated singularities are complete pluripolar. Mich. Math. J. 47, 191–197 (2000)
Zeriahi, A.: Ensembles pluripolaires exceptionels pour la croissance partielle des fonctions holomorphes. Ann. Polon. Math. 50, 81–89 (1989)
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Dieu, N.Q., Hiep, P.H. Pluripolar Hulls and Complete Pluripolar Sets. Potential Anal 29, 409–426 (2008). https://doi.org/10.1007/s11118-008-9103-7
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DOI: https://doi.org/10.1007/s11118-008-9103-7