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Regularity of varieties in strictly pseudoconvex domains.

Franc Forstneric (1988)

Publicacions Matemàtiques

We prove a theorem on the boundary regularity of a purely p-dimensional complex subvariety of a relatively compact, strictly pseudoconvex domain in a Stein manifold. Some applications describing the structure of the polynomial hull of closed curves in Cn are also given.

Riemann surfaces in Stein manifolds with the Density property

Rafael B. Andrist, Erlend Fornæss Wold (2014)

Annales de l’institut Fourier

We show that any open Riemann surface can be properly immersed in any Stein manifold with the (Volume) Density property and of dimension at least 2. If the dimension is at least 3, we can actually choose this immersion to be an embedding. As an application, we show that Stein manifolds with the (Volume) Density property and of dimension at least 3, are characterized among all other complex manifolds by their semigroup of holomorphic endomorphisms.

Runge families and inductive limits of Stein spaces

Andrew Markoe (1977)

Annales de l'institut Fourier

The general Stein union problem is solved: given an increasing sequence of Stein open sets, it is shown that the union X is Stein if and only if H 1 ( X , O X ) is Hausdorff separated.

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