The Michigan Mathematical Journal

Subextension and approximation of negative plurisubharmonic functions

Urban Cegrell and Lisa Hed

Full-text: Open access

Article information

Source
Michigan Math. J., Volume 56, Issue 3 (2008), 593-601.

Dates
First available in Project Euclid: 12 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1231770362

Digital Object Identifier
doi:10.1307/mmj/1231770362

Mathematical Reviews number (MathSciNet)
MR2490648

Zentralblatt MATH identifier
1161.32017

Subjects
Primary: 32U05: Plurisubharmonic functions and generalizations [See also 31C10] 32U15: General pluripotential theory 32W20: Complex Monge-Ampère operators

Citation

Cegrell, Urban; Hed, Lisa. Subextension and approximation of negative plurisubharmonic functions. Michigan Math. J. 56 (2008), no. 3, 593--601. doi:10.1307/mmj/1231770362. https://projecteuclid.org/euclid.mmj/1231770362


Export citation

References

  • S. Benelkourchi, A note on the approximation of plurisubharmonic functions, C. R. Math. Acad. Sci. Paris Sér. I Math. 342 (2006), 647--650.
  • E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1--40.
  • U. Cegrell, Pluricomplex energy, Acta Math. 180 (1998), 187--217.
  • ------, The general definition of the complex Monge--Ampère operator, Ann. Inst. Fourier (Grenoble) 54 (2004), 159--179.
  • ------, Approximation of plurisubharmonic functions in hyperconvex domains, Complex analysis and digital geometry (Proceedings of the Kiselmanfest), Acta Univ. Upsaliensis (to appear).
  • ------, A general Dirichlet problem for the Complex Monge--Ampère operator, Ann. Polon. Math. 94 (2008), 131--147.
  • U. Cegrell and A. Zeriahi, Subextension of plurisubharmonic functions with bounded Monge--Ampère mass, C. R. Math. Acad. Sci. Paris Sér. I Math. 336 (2003), 305--308.
  • J. E. Fornæ ss and J. Wiegerinck, Approximation of plurisubharmonic functions, Ark. Mat. 27 (1989), 257--272.
  • V. K. Nguyen and H. H. Pham, A comparison principle for the complex Monge--Ampère operator in Cegrell's classes and applications, Trans. Amer. Math. Soc. (to appear).
  • H. H. Pham, Pluripolar sets and the subextension in Cegrell's classes, Complex Var. Elliptic Equ. 53 (2008), 675--684.
  • V. Vâjâitu, On locally hyperconvex morphisms, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), 823--828.