Stein structures and holomorphic mappings

Holomorphic Submersions from Stein Manifolds

Holomorphic Submersions from Stein Manifolds

Holomorphic fiber bundle with Stein base and Stein fibers

A surjective holomorphic map Π : X → Y between complex spaces is said to be a Stein morphism, if for every point y ∈ Y , there exists an open neighborhood U of y such that Π(U) is Stein. In 1977, Skoda [12] showed that a locally trivial analytic fiber bundle Π : X → Ω with Stein base and Stein fibers is not necessarily a Stein manifold. Thus giving a negative answer to a conjecture proposed in ...

Holomorphic Invariance of Stein Neighborhood Bases

Let Ω be a smooth bounded pseudoconvex domain in Cn. We give several characterizations for the closure of Ω to have a Stein neighborhood basis in the sense that Ω has a defining function ρ such that {z ∈ Cn : ρ(z) < ε} is pseudoconvex for sufficiently small ε > 0. We also show that this condition is invariant under proper holomorphic maps that extend smoothly to the boundary.

Kolmogorov widths under holomorphic mappings

If L is a bounded linear operator mapping the Banach space X into the Banach space Y and K is a compact set in X, then the Kolmogorov widths of the image L(K) do not exceed those of K multiplied by the norm of L. We extend this result from linear maps to holomorphic mappings u from X to Y in the following sense: when the n widths of K are O(n−r) for some r > 1, then those of u(K) are O(n−s) for...