On uniqueness of solutions to complex Monge-Amp\`ere mean field equations
Complex Variables
2025-01-31 v1 Differential Geometry
Abstract
We establish the uniqueness of solutions to complex Monge-Amp\`ere mean field equations when the temperature parameter is small. In the local setting of bounded hyperconvex domains, our result partially confirms a conjecture by Berman and Berndtsson. Our approach also extends to the global context of compact complex manifolds.
Cite
@article{arxiv.2501.18281,
title = {On uniqueness of solutions to complex Monge-Amp\`ere mean field equations},
author = {Chinh H. Lu and Trong-Thuc Phung},
journal= {arXiv preprint arXiv:2501.18281},
year = {2025}
}