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.
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© 2012 Springer-Verlag Berlin Heidelberg
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Boucksom, S. (2012). Monge–Ampère Equations on Complex Manifolds with Boundary. In: Guedj, V. (eds) Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics. Lecture Notes in Mathematics(), vol 2038. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23669-3_7
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DOI: https://doi.org/10.1007/978-3-642-23669-3_7
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23668-6
Online ISBN: 978-3-642-23669-3
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