The Monge-Ampère equation for non-integrable almost complex structures

Abstract

We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.

38 pages; final version to appear in JEMS

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• On some applications of Gauduchon metrics
• $C^{1,1}$ regularity of degenerate complex Monge-Ampère equations and some applications
• A Metric Lower Bound Estimate for Geodesics in the Space of Kähler Potentials
• Monge-Ampère type equations on almost Hermitian manifolds
• On canonical metrics of complex surfaces with split tangent and related geometric PDEs