Holomorphic Ellipticity vs. Subellipticity: Do the Classes Coincide?

Determine whether, in the holomorphic category, the classes of holomorphically elliptic manifolds and holomorphically subelliptic manifolds coincide.

Background

In the algebraic category, Kaliman and Zaidenberg proved that algebraic subellipticity and algebraic ellipticity coincide, unifying key algebraic Oka properties.

The analogous equivalence in the holomorphic category remains unsettled. Resolving this would clarify the precise landscape of holomorphic flexibility properties and unify the theory across algebraic and analytic settings.