# 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

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topHalil 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

top- [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] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40. Zbl0547.32012
- [3] U. Cegrell and J. Thorbiörnson, Extremal plurisubharmonic functions, Ann. Polon. Math. 63 (1996), 63-69. Zbl0924.31005
- [4] H. I. Celik, Pointwise singularities of plurisubharmonic functions, Ph.D. Thesis, Syracuse University, 1996.
- [5] H. I. Celik and E. A. Poletsky, Order functions of plurisubharmonic functions, Studia Math. 124 (1997), 161-171. Zbl0883.32015
- [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] M. Klimek, Pluripotential Theory, Oxford University Press, New York, 1991.
- [8] E. A. Poletsky, Holomorphic currents, Indiana Univ. Math. J. 42 (1993), 85-144. Zbl0811.32010

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