Integrability of Koszul connections on complex vector bundles over domains in ${\mathbf C}^n$
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912758297001984 |
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| author | Gong, Xianghong |
| author_facet | Gong, Xianghong |
| contents | We study invertible matrix solutions $A$ to the equation $A^{-1}\overline\partial A=ω^{(0,1)}$ on a small open subset $U$ of the closure $\overline M$ of a domain $M\subset{\mathbf C}^n$, where $ω^{(0,1)}$ is a matrix of $(0,1)$ forms on $\overline M$ satisfying the formal integrable condition $\overline{\partial}ω^{(0,1)}=ω^{(0,1)}\wedgeω^{(0,1)}$. For a $C^2$ domain $M$ that is either strongly pseudoconvex or has at least $3$ negative Levi eigenvalues at a boundary point contained in $U$, we obtain existence and sharp regularity of the solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrability of Koszul connections on complex vector bundles over domains in ${\mathbf C}^n$ Gong, Xianghong Complex Variables 32A26, 32F10, 32L05, 32W05, 53B05 We study invertible matrix solutions $A$ to the equation $A^{-1}\overline\partial A=ω^{(0,1)}$ on a small open subset $U$ of the closure $\overline M$ of a domain $M\subset{\mathbf C}^n$, where $ω^{(0,1)}$ is a matrix of $(0,1)$ forms on $\overline M$ satisfying the formal integrable condition $\overline{\partial}ω^{(0,1)}=ω^{(0,1)}\wedgeω^{(0,1)}$. For a $C^2$ domain $M$ that is either strongly pseudoconvex or has at least $3$ negative Levi eigenvalues at a boundary point contained in $U$, we obtain existence and sharp regularity of the solutions. |
| title | Integrability of Koszul connections on complex vector bundles over domains in ${\mathbf C}^n$ |
| topic | Complex Variables 32A26, 32F10, 32L05, 32W05, 53B05 |
| url | https://arxiv.org/abs/2512.10820 |