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arXiv · 2610.10475

A Strong Dominability Criterion and an Oka Union Theorem

Yun-Heng Du·Bin Guo·Peng-Chao Wang·Song-Yan Xie
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Abstract

We prove that an $n$-dimensional complex manifold $Y$ is Oka if and only if it is strongly dominable: for every $y\in Y$, there is an entire map $F:\mathbb{C}^n\to Y$ such that $F(0)=y$ and $dF_0$ is invertible. The argument converts this pointwise domination into the convex approximation property in every source dimension. We also show that the Oka property extends across proper closed complex analytic subsets: if $A$ is such a subset of a connected complex manifold $X$ and $X\setminus A$ is Oka, then $X$ is Oka. The criterion has broad applications and produces many new examples of Oka manifolds.

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Yun-Heng Du, Bin Guo, Peng-Chao Wang, Song-Yan Xie. 2026-10-07. A Strong Dominability Criterion and an Oka Union Theorem. https://arxiv.org/abs/2610.10475

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