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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.05352 |
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| _version_ | 1866908680328314880 |
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| author | Pan, Changpeng |
| author_facet | Pan, Changpeng |
| contents | For any Hermitian holomorphic vector bundle with Nakano positive curvature tensor, Demailly introduced a Monge-Ampère type equation. When the rank of the bundle is $1$, it becomes the usual Monge-Ampère equation. In this paper, we solve this equation in the conformal class of a Nakano positive Hermitian metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05352 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monge-Ampère type equation for the Nakano positive curvature tensor of holomorphic vector bundles Pan, Changpeng Differential Geometry Analysis of PDEs For any Hermitian holomorphic vector bundle with Nakano positive curvature tensor, Demailly introduced a Monge-Ampère type equation. When the rank of the bundle is $1$, it becomes the usual Monge-Ampère equation. In this paper, we solve this equation in the conformal class of a Nakano positive Hermitian metric. |
| title | Monge-Ampère type equation for the Nakano positive curvature tensor of holomorphic vector bundles |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2501.05352 |