An iterative approach to the complex Monge–Ampère eigenvalue problem
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 $\mathbb C^n$. This approach is inspired by a similar approach initiated by F. Abedin and J. Kitagawa (2020) who considered the real Monge–Ampère operator on a strictly convex domain in $\mathbb R^N$. This work is based on recent results obtained by P. Badiane and the author on the existence and uniqueness of the solution to the Dirichlet eigenvalue problem for the complex Monge–Ampère operator. However, the iterative approach does not require the a priori knowledge of the first eigenvalue but it provides an effective scheme for approximating it, as well as the associated eigenfunction.
