Some variational problems for the complex Monge--Amp{\`e}re operator
Complex Variables
2026-04-16 v1 Analysis of PDEs
Differential Geometry
Abstract
We consider the Dirichlet problem for the complex Monge--Amp\`ere equation on strongly pseudoconvex K\"ahler manifolds when the right-hand side is decreasing in the solution. Using flow-based arguments, we establish existence of smooth solutions in a number of natural circumstances, following work of Chou-Wang.
Cite
@article{arxiv.2604.13421,
title = {Some variational problems for the complex Monge--Amp{\`e}re operator},
author = {Jianchun Chu and Yaxiong Liu and Nicholas McCleerey and Weijun Zhang},
journal= {arXiv preprint arXiv:2604.13421},
year = {2026}
}