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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 \(\overline \Omega\) be a compact strongly pseudoconvex domain with smooth boundary in a Stein manifold, and let \(h:Z\to \overline \Omega\) be a fibre bundle of H\"older-Zygmund class \(\Lambda^r\), \(r>0\), which is holomorphic over \(\Omega\). Assuming that the fibre is an Oka manifold, we prove that every continuous section \(f_0:\overline \Omega\to Z\) is homotopic to a section \(f_1:\overline \Omega\to Z\) of class \(\Lambda^r(\overline \Omega)\) which is holomorphic on \(\Omega\). 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 H\"older-Zygmund classes on such domains.

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Franc Forstneric. 2026-02-13. 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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