A \mathcal C^2,α estimate of the complex Monge-Ampère equation

2017/05/24 by Chao Li, Jiayu Li, Li, Chao +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Alpha (finance) #BETA (programming language) #Bar (unit) #Combinatorics #Computer science #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical physics #Mathematics #Physics #Statistics #math.DG

paper · pdf · doi:10.48550/arxiv.1705.08634

published in arXiv (Cornell University) (Cornell University)

arxiv created 2017/05/24 · openalex publication_date 2017/05/24 · arxiv updated 2017/05/25 · openalex created_date 2017/06/05 · openalex updated_date 2026/08/05

Abstract

In this paper, we prove a \mathcal C^2,α-estimate for the solution to the complex Monge-Ampère equation det(u_ij)=f with 0< f∈ \mathcal C^α, under the assumption that u∈ \mathcal C^1,β for some β<1 which depends on n and α.

Citations

• Elliptic Partial Differential Equations of Second Order
• On the existence of a complete Kähler metric on non‐compact complex manifolds and the regularity of fefferman's equation
• On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I
• Complete Kähler manifolds with zero Ricci curvature. I

Cited by

• Scalar curvature and properness on Sasaki manifolds

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