Hermitian-Einstein equations on noncompact manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916469812494336 |
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| author | Wu, Di Zhang, Xi |
| author_facet | Wu, Di Zhang, Xi |
| contents | This paper first investigates solvability of Hermitian-Einstein equation on a Hermitian holomorphic vector bundle on the complement of an arbitrary closed subset in a compact Hermitian manifold. The uniqueness of Hermitian-Einstein metrics on a Zariski open subset in a compact Kähler manifold was only figured out by Takuro Mochizuki recently, for this model the second part of this paper gives an affirmative answer to a question proposed by Takuro Mochizuki and it leads to an alternative approach to the unique issue. We also prove stability from solvability of Hermitian-Einstein equation, which together with the classical existence result of Carlos Simpson in particular establish a Kobayashi-Hitchin bijective correspondence. The argument is also effective in more general settings, including basic models of Takuro Mochizuki, as well as non-Kähler and semi-stable contexts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hermitian-Einstein equations on noncompact manifolds Wu, Di Zhang, Xi Differential Geometry Analysis of PDEs 53C07, 14J60 This paper first investigates solvability of Hermitian-Einstein equation on a Hermitian holomorphic vector bundle on the complement of an arbitrary closed subset in a compact Hermitian manifold. The uniqueness of Hermitian-Einstein metrics on a Zariski open subset in a compact Kähler manifold was only figured out by Takuro Mochizuki recently, for this model the second part of this paper gives an affirmative answer to a question proposed by Takuro Mochizuki and it leads to an alternative approach to the unique issue. We also prove stability from solvability of Hermitian-Einstein equation, which together with the classical existence result of Carlos Simpson in particular establish a Kobayashi-Hitchin bijective correspondence. The argument is also effective in more general settings, including basic models of Takuro Mochizuki, as well as non-Kähler and semi-stable contexts. |
| title | Hermitian-Einstein equations on noncompact manifolds |
| topic | Differential Geometry Analysis of PDEs 53C07, 14J60 |
| url | https://arxiv.org/abs/2406.11449 |