Radially symmetric plurisubharmonic functions
Volume 106 / 2012
Annales Polonici Mathematici 106 (2012), 1-17
MSC: Primary 32U05, 32W20; Secondary 31B05.
DOI: 10.4064/ap106-0-1
Abstract
In this note we consider radially symmetric plurisubharmonic functions and the complex Monge–Ampère operator. We prove among other things a complete characterization of unitary invariant measures for which there exists a solution of the complex Monge–Ampère equation in the set of radially symmetric plurisubharmonic functions. Furthermore, we prove in contrast to the general case that the complex Monge–Ampère operator is continuous on the set of radially symmetric plurisubharmonic functions. Finally we characterize radially symmetric plurisubharmonic functions among the subharmonic ones using merely the laplacian.
