Fundamental solutions of the complex Monge-Ampère equation

Halil Ibrahim Celik; Evgeny A. Poletsky

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 2, page 103-110
  • ISSN: 0066-2216

Abstract

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We prove that any positive function on ℂℙ¹ which is constant outside a countable G δ -set is the order function of a fundamental solution of the complex Monge-Ampère equation on the unit ball in ℂ² with a singularity at the origin.

How to cite

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Halil Ibrahim Celik, and Evgeny A. Poletsky. "Fundamental solutions of the complex Monge-Ampère equation." Annales Polonici Mathematici 67.2 (1997): 103-110. <http://eudml.org/doc/270695>.

@article{HalilIbrahimCelik1997,
abstract = {We prove that any positive function on ℂℙ¹ which is constant outside a countable $G_δ$-set is the order function of a fundamental solution of the complex Monge-Ampère equation on the unit ball in ℂ² with a singularity at the origin.},
author = {Halil Ibrahim Celik, Evgeny A. Poletsky},
journal = {Annales Polonici Mathematici},
keywords = {plurisubharmonic functions; singularities; order function; Monge-Ampère equation; Monge-Ampère operator; fundamental solution},
language = {eng},
number = {2},
pages = {103-110},
title = {Fundamental solutions of the complex Monge-Ampère equation},
url = {http://eudml.org/doc/270695},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Halil Ibrahim Celik
AU - Evgeny A. Poletsky
TI - Fundamental solutions of the complex Monge-Ampère equation
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 2
SP - 103
EP - 110
AB - We prove that any positive function on ℂℙ¹ which is constant outside a countable $G_δ$-set is the order function of a fundamental solution of the complex Monge-Ampère equation on the unit ball in ℂ² with a singularity at the origin.
LA - eng
KW - plurisubharmonic functions; singularities; order function; Monge-Ampère equation; Monge-Ampère operator; fundamental solution
UR - http://eudml.org/doc/270695
ER -

References

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  1. [1] E. Bedford and B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math. 37 (1976), 19-22. Zbl0315.31007
  2. [2] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40. Zbl0547.32012
  3. [3] U. Cegrell and J. Thorbiörnson, Extremal plurisubharmonic functions, Ann. Polon. Math. 63 (1996), 63-69. Zbl0924.31005
  4. [4] H. I. Celik, Pointwise singularities of plurisubharmonic functions, Ph.D. Thesis, Syracuse University, 1996. 
  5. [5] H. I. Celik and E. A. Poletsky, Order functions of plurisubharmonic functions, Studia Math. 124 (1997), 161-171. Zbl0883.32015
  6. [6] J. P. Demailly, Monge-Ampère operators, Lelong numbers and intersection theory, in: Complex Analysis and Geometry, Plenum Press, New York, 1993, 115-193. Zbl0792.32006
  7. [7] M. Klimek, Pluripotential Theory, Oxford University Press, New York, 1991. 
  8. [8] E. A. Poletsky, Holomorphic currents, Indiana Univ. Math. J. 42 (1993), 85-144. Zbl0811.32010

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