Closure of the Oka Class under Strong Dominability

Ascertain whether the class of Oka manifolds is closed under strong dominability, or at least Hausdorff-local, thereby determining if Oka-type properties persist under local strong dominability conditions.

Background

The authors define a class C obtained by closing the class of Oka manifolds with respect to strong dominability and prove that every manifold in C enjoys LSAP and hence the Oka‑1 property (Theorem 1.11).

Whether the original Oka class itself is closed under strong dominability (or even just Hausdorff-local) remains open and is central to understanding the robustness of Oka-type properties under local holomorphic domination.