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Mathematics > Differential Geometry

arXiv:0710.5109 (math)
[Submitted on 26 Oct 2007 (v1), last revised 24 Mar 2009 (this version, v3)]

Title:Degenerate complex Monge-Ampère equations over compact Kähler manifolds

Authors:Jean-Pierre Demailly, Nefton Pali
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Abstract: We prove the existence and uniqueness of the solutions of some very general type of degenerate complex Monge-Ampère equations. This type of equations is precisely what is needed in order to construct Kähler-Einstein metrics over irreducible singular Kähler spaces with ample or trivial canonical sheaf and singular Kähler-Einstein metrics over varieties of general type.
Comments: The present manuscript expands and completes a paper accepted for publication in the International Journal of Mathematics, which had to be shortened in view of the length of the manuscript and of the demands of referees - in particular it gives more details about the relation with the existing litterature (see Appendix C)
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:0710.5109 [math.DG]
  (or arXiv:0710.5109v3 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.5109

Submission history

From: Nefton Pali [view email]
[v1] Fri, 26 Oct 2007 14:55:12 UTC (38 KB)
[v2] Thu, 6 Dec 2007 10:31:56 UTC (41 KB)
[v3] Tue, 24 Mar 2009 20:35:26 UTC (49 KB)
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