We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.
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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.
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