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Journal of the London Mathematical Society 2005 72(1):225-238; doi:10.1112/S0024610705006460
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© The London Mathematical Society

The Set of Measures Given by Bounded Solutions of the Complex Monge–Ampère Equation on Compact Kähler Manifolds

Slawomir Kolodziej

Institute of Mathematics, Jagiellonian University Reymonta 4, 30-059 Kraków, Poland kolodzie{at}im.uj.edu.pl

Received 15 January 2004. Revision received 23 September 2004.

Consider the image of the Monge–Ampère operator acting on bounded functions, defined on a compact Kähler manifold, whose sum with the local Kähler potential is plurisubharmonic. It is shown that a nonnegative Borel measure belongs to this image if and only if it belongs to the image locally. In particular, those measures form a convex set.


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