On Pointwise Gradient Estimates for the Complex Monge-Ampere Equation

2009/11/15 by D. H. Phong, Phong, D. H., Jacob Sturm +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0911.2881

openalex publication_date 2009/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, a gradient estimate for the complex Monge-Ampere equation is established. It differs from previous estimates of Yau, Hanani, Blocki, P. Guan, B. Guan - Q. Li in that it is pointwise, and depends only on the infimum of the solution instead of its C⁰ norm.

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