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arXiv · 2501.18281

On uniqueness of solutions to complex Monge-Amp\`ere mean field equations

Chinh H. Lu·Trong-Thuc Phung
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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.

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Chinh H. Lu, Trong-Thuc Phung. 2025-01-30. On uniqueness of solutions to complex Monge-Amp\`ere mean field equations. https://arxiv.org/abs/2501.18281

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