English

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.

Keywords

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}
}