An Iterative Approach to the Complex Monge-Amp\`ere Eigenvalue Problem

TL;DR

This paper introduces an iterative method to approximate solutions to the complex Monge-Ampère eigenvalue problem on pseudoconvex domains, extending ideas from real Monge-Ampère operators.

Contribution

It develops a novel iterative approach for the complex Monge-Ampère eigenvalue problem, inspired by methods used for the real Monge-Ampère operator.

Findings

Proposes an iterative scheme for the complex Monge-Ampère eigenvalue problem.

Extends real Monge-Ampère techniques to complex domains.

Provides theoretical foundation for convergence of the method.

Abstract

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