On uniqueness of solutions to complex Monge-Ampère mean field equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866909470126243840 |
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| author | Lu, Chinh H. Phung, Trong-Thuc |
| author_facet | Lu, Chinh H. Phung, Trong-Thuc |
| contents | We establish the uniqueness of solutions to complex Monge-Ampère 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18281 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On uniqueness of solutions to complex Monge-Ampère mean field equations Lu, Chinh H. Phung, Trong-Thuc Complex Variables Differential Geometry We establish the uniqueness of solutions to complex Monge-Ampère 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. |
| title | On uniqueness of solutions to complex Monge-Ampère mean field equations |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2501.18281 |