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Monge–Ampère Equations on Complex Manifolds with Boundary

  • Sébastien Boucksom
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2038)

Abstract

We survey the proofs of two fundamental results on the resolution of Monge–Ampère equations on complex manifolds with boundary. The first result guarantees the existence of smooth solutions to non-degenerate com- plex Monge–Ampère equations admitting subsolutions, it is a continuation of results due to Caffarelli–Kohn–Nirenberg–Spruck. The second result shows the existence of almost C2 solutions to degenerate complex Monge–Ampère equations admitting subsolutions and yields as a special case X.X.Chen’s result on the existence of almost C2 geodesics in spaces of Kähler metrics.

Keywords

Maximum Principle Complex Manifold Ahler Manifold Compact Riemann Surface Elliptic Regularity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.CNRS et Institut de Mathématiques de JussieuUniversité Pierre et Marie CurieParis Cedex 05France

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