The complex Monge–Ampère equation for complex homogeneous functions in ${\mathbb C}^n$

Volume 76 / 2001

Rafał Czyż Annales Polonici Mathematici 76 (2001), 287-302 MSC: Primary 32U15, 32W20; Secondary 32Q20. DOI: 10.4064/ap76-3-7


We prove some existence results for the complex Monge–Ampère equation $(dd^cu)^n =gd\lambda $ in ${\mathbb C}^n $ in a certain class of homogeneous functions in ${\mathbb C}^n $, 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.


  • Rafał CzyżDepartment of Mathematics
    Jagiellonian University
    Reymonta 4
    30-059 Krak/ow, Poland

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