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The Set of Measures Given by Bounded Solutions of the Complex Monge–Ampère Equation on Compact Kähler Manifolds
Author(s) -
Kołodziej Sławomir
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705006460
Subject(s) - mathematics , bounded function , image (mathematics) , compact space , pure mathematics , measure (data warehouse) , manifold (fluid mechanics) , operator (biology) , kähler manifold , monge–ampère equation , mathematical analysis , set (abstract data type) , regular polygon , riemannian manifold , complex manifold , geometry , mechanical engineering , biochemistry , chemistry , repressor , database , computer science , transcription factor , engineering , gene , programming language , holomorphic function , artificial intelligence
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.