The general definition of the complex Monge-Ampère operator

Urban Cegrell[1]

  • [1] Umeå University, Department of Mathematics, 901 87 Umeå (Suède)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 1, page 159-179
  • ISSN: 0373-0956

Abstract

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We define and study the domain of definition for the complex Monge-Ampère operator. This domain is the most general if we require the operator to be continuous under decreasing limits. The domain is given in terms of approximation by certain " test"-plurisubharmonic functions. We prove estimates, study of decomposition theorem for positive measures and solve a Dirichlet problem.

How to cite

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Cegrell, Urban. "The general definition of the complex Monge-Ampère operator." Annales de l’institut Fourier 54.1 (2004): 159-179. <http://eudml.org/doc/116103>.

@article{Cegrell2004,
abstract = {We define and study the domain of definition for the complex Monge-Ampère operator. This domain is the most general if we require the operator to be continuous under decreasing limits. The domain is given in terms of approximation by certain " test"-plurisubharmonic functions. We prove estimates, study of decomposition theorem for positive measures and solve a Dirichlet problem.},
affiliation = {Umeå University, Department of Mathematics, 901 87 Umeå (Suède)},
author = {Cegrell, Urban},
journal = {Annales de l’institut Fourier},
keywords = {complex Monge-Ampère operator; plurisubharmonic function; Monge-Ampère operator; test functions; weak*-convergence; Dirichlet problem; pluripolar set},
language = {eng},
number = {1},
pages = {159-179},
publisher = {Association des Annales de l'Institut Fourier},
title = {The general definition of the complex Monge-Ampère operator},
url = {http://eudml.org/doc/116103},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Cegrell, Urban
TI - The general definition of the complex Monge-Ampère operator
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 1
SP - 159
EP - 179
AB - We define and study the domain of definition for the complex Monge-Ampère operator. This domain is the most general if we require the operator to be continuous under decreasing limits. The domain is given in terms of approximation by certain " test"-plurisubharmonic functions. We prove estimates, study of decomposition theorem for positive measures and solve a Dirichlet problem.
LA - eng
KW - complex Monge-Ampère operator; plurisubharmonic function; Monge-Ampère operator; test functions; weak*-convergence; Dirichlet problem; pluripolar set
UR - http://eudml.org/doc/116103
ER -

References

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