The complex Monge-Ampère equation and pluripotential theory
著者
書誌事項
The complex Monge-Ampère equation and pluripotential theory
（Memoirs of the American Mathematical Society, no. 840）
American Mathematical Society, 2005
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注記
"November 2005, Volume 178, number 840 (fourth of 5 numbers)."
Includes bibliographical references (p. 63-64)
内容説明・目次
内容説明
We collect here results on the existence and stability of weak solutions of complex Monge-Ampere equation proved by applying pluripotential theory methods and obtained in past three decades. First we set the stage introducing basic concepts and theorems of pluripotential theory. Then the Dirichlet problem for the complex Monge-Ampere equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part, the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampere equation on compact Kahler manifolds. This is a generalization of the Calabi-Yau theorem.
目次
Positive currents and plurisubharmonic functions Siciak's extremal function and a related capacity The Dirichlet problem for the Monge-Ampere equation with continuous data The Dirichlet problem continued The Monge-Ampere equation for unbounded functions The complex Monge-Ampere equation on a compact Kahler manifold Bibliography.
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