An energy estimate for the complex Monge-Ampère operator

Urban Cegrell; Leif Persson

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 1, page 95-102
  • ISSN: 0066-2216

Abstract

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We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.

How to cite

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Urban Cegrell, and Leif Persson. "An energy estimate for the complex Monge-Ampère operator." Annales Polonici Mathematici 67.1 (1997): 95-102. <http://eudml.org/doc/270248>.

@article{UrbanCegrell1997,
abstract = {We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.},
author = {Urban Cegrell, Leif Persson},
journal = {Annales Polonici Mathematici},
keywords = {capacity; complex Monge-Ampère operator; energy estimate; plurisubharmonic function; comparison theorem},
language = {eng},
number = {1},
pages = {95-102},
title = {An energy estimate for the complex Monge-Ampère operator},
url = {http://eudml.org/doc/270248},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Urban Cegrell
AU - Leif Persson
TI - An energy estimate for the complex Monge-Ampère operator
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 1
SP - 95
EP - 102
AB - We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.
LA - eng
KW - capacity; complex Monge-Ampère operator; energy estimate; plurisubharmonic function; comparison theorem
UR - http://eudml.org/doc/270248
ER -

References

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  1. [1] E. Bedford, Survey of pluri-potential theory, in: Several Complex Variables, Proc. Mittag-Leffler Institute, 1987-88, J. E. Fornaess (ed.), Math. Notes 38, Princeton Univ. Press, 1993, 48-97. 
  2. [2] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40. Zbl0547.32012
  3. [3] L. Carleson, Selected Problems on Exceptional Sets, Van Nostrand, Princeton, N.J., 1967. 
  4. [4] U. Cegrell, The symmetric pluricomplex Green function, in: Banach Center Publ. 31, Inst. Math., Polish Acad. Sci., Warszawa, 1995, 135-141. Zbl0831.31008
  5. [5] U. Cegrell, Pluricomplex energy, Acta Math., to appear. Zbl40.0098.04
  6. [6] N. S. Landkof, Foundations of Modern Potential Theory, Springer, 1972. 
  7. [7] L. Persson, A Dirichlet principle for the complex Monge-Ampère operator, Research Report No. 8, 1997, Dept. Math., Umeå University. Zbl1045.34056

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