12 citations · 49 across the 10 of their papers we have counts for
9 papers · 1 filter
Oka realizations, fundamental groups, and holomorphic cofibrations
Bin Guo, Yuta Kusakabe, Peng-Chao Wang
The homotopy types of Oka manifolds are exactly those of countable finite-dimensional CW complexes. We construct realizations as open subsets of complex Euclidean spaces with expli…
Oka Geometry of Complex Six-Spheres
Yun-Heng Du, Bin Guo, Yuta Kusakabe +1
Alpöge constructed a complex structure on through a torus fibration with exactly three special fibres. We prove that every member of the associated admissible period family i…
Oka tubes in holomorphic line bundles
Franc Forstneric, Yuta Kusakabe
Let be a semipositive hermitian holomorphic line bundle on a compact complex manifold with . Assume that for each point there exists a divisor $D\in…
Oka properties of complements of holomorphically convex sets
Yuta Kusakabe
Our main theorem states that the complement of a compact holomorphically convex set in a Stein manifold with the density property is an Oka manifold. This gives a positive answer t…
An implicit function theorem for sprays and applications to Oka theory
Yuta Kusakabe
We solve fundamental problems in Oka theory by establishing an implicit function theorem for sprays. As the first application of our implicit function theorem, we obtain an element…
Elliptic characterization and unification of Oka maps
Yuta Kusakabe
We generalize our elliptic characterization of Oka manifolds to Oka maps. The generalized characterization can be considered as an affirmative answer to the relative version of Gro…
Oka complements of countable sets and non-elliptic Oka manifolds
Yuta Kusakabe
We study the Oka properties of complements of closed countable sets in which are not necessarily discrete. Our main result states that every tame closed cou…
Elliptic characterization and localization of Oka manifolds
Yuta Kusakabe
We prove that Gromov's ellipticity condition characterizes Oka manifolds. This characterization gives another proof of the fact that subellipticity implies the Oka…
Dense holomorphic curves in spaces of holomorphic maps and applications to universal maps
Yuta Kusakabe
We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. We first show that for any bounded convex domain and…