The conical complex Monge-Ampère equations on Kähler manifolds

2016/09/13 by Jiawei Liu, Liu, Jiawei, Chuanjing Zhang +1
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1609.03821

openalex publication_date 2016/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, by providing the uniform gradient estimates for a sequence of the approximating equations, we prove the existence, uniqueness and regularity of the conical parabolic complex Monge-Ampère equation with weak initial data. As an application, we prove a regularity estimates, that is, any L^∞-solution of the conical complex Monge-Ampère equation admits the C^2,α,β-regularity.

Related

• The complex Monge-Ampere equation on compact Kaehler manifolds
• Parabolic complex Monge-Ampere equations on compact Kahler manifolds
• Regularity of A Complex Monge-Ampère Equation on Hermitian Manifolds
• Geometric estimates for complex Monge-Ampere equations
• On regularity of complex Monge-Ampere equation