An Iterative Approach to the Complex Monge-Ampère Eigenvalue Problem

2025/07/17 by Ahmed Zériahi, Zeriahi, Ahmed · 1 citation
Mathematics · #31C45 #32U15 #32U40 #32W20 #35J66 #35J96 #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2507.13273

openalex publication_date 2025/07/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We present an iterative approach to approximate the solution to the Dirichlet complex Monge-Ampère eigenvalue problem on a bounded strictly pseudoconvex domain in \Cⁿ. This approach is inspired by a similar approach initiated by F. Abedin, J. Kitagawa who considered the real Monge-Ampère operator on a strictly convex domain in \R^N.

Citations

• The Eigenvalue Problem for the Complex Hessian Operator on m-Pseudoconvex Manifolds
• A variational approach to complex Monge-Ampere equations

Cited by

• A new approach to the Monge-Ampère eigenvalue problem

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