The complex Monge-Ampère equation for complex homogeneous functions in ℂⁿ

Rafał Czyż

The complex Monge-Ampère equation for complex homogeneous functions in ℂⁿ

Rafał Czyż

Annales Polonici Mathematici (2001)

Volume: 76, Issue: 3, page 287-302
ISSN: 0066-2216

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Abstract

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We prove some existence results for the complex Monge-Ampère equation

(d d^{c} u) ⁿ = g d λ

in ℂⁿ in a certain class of homogeneous functions in ℂⁿ, i.e. we show that for some nonnegative complex homogeneous functions g there exists a plurisubharmonic complex homogeneous solution u of the complex Monge-Ampère equation.

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Rafał Czyż. "The complex Monge-Ampère equation for complex homogeneous functions in ℂⁿ." Annales Polonici Mathematici 76.3 (2001): 287-302. <http://eudml.org/doc/280997>.

@article{RafałCzyż2001,
abstract = {We prove some existence results for the complex Monge-Ampère equation $(dd^cu)ⁿ = gdλ$ in ℂⁿ in a certain class of homogeneous functions in ℂⁿ, i.e. we show that for some nonnegative complex homogeneous functions g there exists a plurisubharmonic complex homogeneous solution u of the complex Monge-Ampère equation.},
author = {Rafał Czyż},
journal = {Annales Polonici Mathematici},
keywords = {complex Monge-Ampère equation; homogeneous plurisubharmonic function; Kähler-Einstein manifold},
language = {eng},
number = {3},
pages = {287-302},
title = {The complex Monge-Ampère equation for complex homogeneous functions in ℂⁿ},
url = {http://eudml.org/doc/280997},
volume = {76},
year = {2001},
}

TY - JOUR
AU - Rafał Czyż
TI - The complex Monge-Ampère equation for complex homogeneous functions in ℂⁿ
JO - Annales Polonici Mathematici
PY - 2001
VL - 76
IS - 3
SP - 287
EP - 302
AB - We prove some existence results for the complex Monge-Ampère equation $(dd^cu)ⁿ = gdλ$ in ℂⁿ in a certain class of homogeneous functions in ℂⁿ, i.e. we show that for some nonnegative complex homogeneous functions g there exists a plurisubharmonic complex homogeneous solution u of the complex Monge-Ampère equation.
LA - eng
KW - complex Monge-Ampère equation; homogeneous plurisubharmonic function; Kähler-Einstein manifold
UR - http://eudml.org/doc/280997
ER -

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