The Oka principle for holomorphic fibre bundles of Holder-Zygmund classes on strongly pseudoconvex domains

Franc Forstneric

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arXiv · 2602.12598

The Oka principle for holomorphic fibre bundles of Holder-Zygmund classes on strongly pseudoconvex domains

Franc Forstneric

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Abstract

Let $\overline Ω$ be a compact strongly pseudoconvex domain with smooth boundary in a Stein manifold, and let $h:Z\to \overline Ω$ be a fibre bundle of Hölder-Zygmund class $Λ^r$, $r>0$, which is holomorphic over $Ω$. Assuming that the fibre is an Oka manifold, we prove that every continuous section $f_0:\overline Ω\to Z$ is homotopic to a section $f_1:\overline Ω\to Z$ of class $Λ^r(\overline Ω)$ which is holomorphic on $Ω$. We also establish the parametric h-principle in this context. As an application, we obtain the Oka principle for the classification of vector bundles and principal bundles of Hölder-Zygmund classes on such domains.

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BibTeX RIS

Franc Forstneric. 2026-09-14. The Oka principle for holomorphic fibre bundles of Holder-Zygmund classes on strongly pseudoconvex domains. https://arxiv.org/abs/2602.12598

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