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Order functions of plurisubharmonic functions

Halil Celik; Evgeny Poletsky — 1997

Studia Mathematica

We consider the following problem: find on $ℂ^{2}$ a plurisubharmonic function with a given order function. In particular, we prove that any positive ambiguous function on $ℂ ℙ^{1}$ which is constant outside a polar set is the order function of a plurisubharmonic function.

Fundamental solutions of the complex Monge-Ampère equation

Halil Ibrahim Celik; Evgeny A. Poletsky — 1997

Annales Polonici Mathematici

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.

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