Characterizing the range of the complex Monge-Ampère operator
arXiv:2412.03445
Abstract
In this note, we solve the complex Monge-Ampère equation for measures with a pluripolar part in compact Kähler manifolds. This result generalizes the classical results obtained by Cegrell in bounded hyperconvex domains. We also discuss the properties of the complex Monge-Ampère operator in some special cases.
arXiv comment11 pages, no figures. v1. comments are welcome. v3 The main result remains unchanged, and the length of the paper has been reduced