On a generalized Monge-Ampère equation on closed almost Kähler surfaces

2024/12/24 by Ken Wang, Wang, Ken, Zuyi Zhang +5
Mathematics · #32Q60 #53C56 #53C65 #53D35 #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2412.18361

openalex publication_date 2024/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show the existence and uniqueness of solutions to a generalized Monge-Ampère equation on closed almost Kähler surfaces, where the equation depends only on the underlying almost Kähler structure. As an application, we prove Donaldson's conjecture for tamed almost complex 4-manifolds.

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