A general comparison principle for the pluripotential complex Monge-Ampère flow

2025/11/09 by Kang, Bowoo
Mathematics · #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2511.06412

openalex publication_date 2025/11/09 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

We prove a comparison principle for the pluripotential complex Monge-Ampère flows for the right-hand side of the form dt \wedge dμ where dμ is dominated by a Monge-Ampère measure of a bounded plurisubharmonic function. As a consequence, we obtain the uniqueness of the weak solution to the pluripotential Cauchy-Dirichlet problem. We also study the long-term behavior of the solution under some assumption.

Citations

• The Pluripotential Cauchy-Dirichlet problem for the Complex Monge-Ampère flow with a general measure on the right-hand side
• A comparison principle for parabolic complex Monge-Ampère equations
• Parabolic complex Monge-Ampère equations on compact Hermitian manifolds
• Pluripotential solutions versus viscosity solutions to complex Monge-Ampère flows
• Parabolic complex Monge-Ampere equations on compact Kahler manifolds
• Viscosity solutions to parabolic complex Monge-Ampère equations
• The pluripotential Cauchy-Dirichlet problem for complex Monge-Ampere flows
• Fully non-linear parabolic equations on compact Hermitian manifolds
• Weak subsolutions to complex Monge-Ampère equations
• Weak solutions to degenerate complex Monge-Ampére flows I
• The Kahler-Ricci flow through singularities
• On stability and the convergence of the Kähler-Ricci flow

Related

• The Pluripotential Cauchy-Dirichlet problem for the Complex Monge-Ampère flow with a general measure on the right-hand side
• A strong comparison principle for the generalized Dirichlet problem for Monge-Ampere
• A comparison principle for parabolic complex Monge-Ampère equations
• The pluripotential Cauchy-Dirichlet problem for complex Monge-Ampere flows
• Pluripotential solutions versus viscosity solutions to complex Monge-Ampère flows