The set of measures given by bounded solutions of the complex Monge-Ampère equation on compact Kähler manifolds

• Autores: Slawomir Kolodziej
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 72, Nº 1, 2005, págs. 225-238
• Idioma: inglés
• DOI: 10.1112/s0024610705006460
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• Resumen

  • 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.