Integrability of Koszul connections on complex vector bundles over domains in ${\mathbf C}^n$

Xianghong Gong

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arXiv · 2512.10820

Integrability of Koszul connections on complex vector bundles over domains in ${\mathbf C}^n$

Xianghong Gong

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Abstract

We study invertible matrix solutions $A$ to the equation $A^{-1}\overline\partial A=\omega^{(0,1)}$ on a small open subset $U$ of the closure $\overline M$ of a domain $M\subset{\mathbf C}^n$, where $\omega^{(0,1)}$ is a matrix of $(0,1)$ forms on $\overline M$ satisfying the formal integrable condition $\overline{\partial}\omega^{(0,1)}=\omega^{(0,1)}\wedge\omega^{(0,1)}$. 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.

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BibTeX RIS

Xianghong Gong. 2025-12-11. Integrability of Koszul connections on complex vector bundles over domains in ${\mathbf C}^n$. https://arxiv.org/abs/2512.10820

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