Author

Yuta Kusakabe

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Preprint Oct 2026

Atiyah classes and ellipticity of Oka manifolds

We prove that every weakly pseudoconvex Oka manifold admitting a positive line bundle is elliptic in the sense of Gromov, thereby proving Gromov's ellipticity conjecture. The proof establishes a cohomological construction of local sprays. Given a bundle morphism $\varphi\colon E\to T_X$, we introduce quadratic $\varphi...

Yuta Kusakabe, Shin-ichi Matsumura · 1 citation

Preprint Oct 2026

Every Gromov elliptic domain is meromorphically pseudoconvex

We prove that every Gromov elliptic domain $\Omega$ in a complex manifold has the following property, which we call meromorphic pseudoconvexity: each boundary point has a neighborhood $V$ such that $\Omega\cap V$ becomes Stein after removing a set which is, locally in $\Omega\cap V$, the union of the polar sets of fini...

Yuta Kusakabe · 0 citations

Preprint Sep 2026

Oka Geometry and Deformations of Torus-Fibred Complex Six-Spheres

Starting from Alp\"oge's torus fibration with exactly three special fibres on a complex six-sphere, we construct a locally miniversal family of compact complex threefolds. Every member is Oka, and the projection over each relatively compact parameter disc is an Oka map. Deleting or simultaneously blowing up finitely ma...

Yun Du, Bin Guo, Yuta Kusakabe et al. · 1 citation