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arXiv · 2604.13421

Some variational problems for the complex Monge--Amp{\`e}re operator

Jianchun Chu·Yaxiong Liu·Nicholas McCleerey·Weijun Zhang
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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.

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Jianchun Chu, Yaxiong Liu, Nicholas McCleerey, Weijun Zhang. 2026-04-15. Some variational problems for the complex Monge--Amp{\`e}re operator. https://arxiv.org/abs/2604.13421

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