Regularity of A Complex Monge-Ampère Equation on Hermitian Manifolds

2013/11/18 by Xiaolan Nie, Nie, Xiaolan
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1311.4463

16 pages

arxiv created 2013/11/18 · openalex publication_date 2013/11/18 · arxiv updated 2013/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain higher order estimates for a parabolic flow on a compact Hermitian manifold. As an application, we prove that a bounded ω-plurisubharmonic solution of an elliptic complex Monge-Ampère equation is smooth under an assumption on the background Hermitian metric ω. This generalizes a result of Székelyhidi and Tosatti on Kähler manifolds.

Citations

• Complex Monge-Ampere equations on Hermitian manifolds

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