Euclidean domains in complex manifolds

  title={Euclidean domains in complex manifolds},
  author={Franc Forstneri{\vc}},
  journal={Journal of Mathematical Analysis and Applications},
  • F. Forstnerič
  • Published 7 April 2021
  • Mathematics
  • Journal of Mathematical Analysis and Applications

Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets

In this paper we construct open Stein neighbourhoods of compact sets of the form A ∪ K in a complex space, where K is a compact holomorphically convex set, A is a compact complex curve with boundary

Recent developments on Oka manifolds

A BSTRACT . This paper is a survey of developments in Oka theory since the publication of my book Stein Manifolds and Holomorphic Mappings (The Homotopy Principle in Complex Analysis) , Second



Strongly pseudoconvex domains as subvarieties of complex manifolds

In this paper we obtain existence and approximation results for closed complex subvarieties that are normalized by strongly pseudoconvex Stein domains. Our sufficient condition for the existence of

Interpolation by holomorphic automorphisms and embeddings in Cn

Let n > 1 and letCndenote the complex n-dimensional Euclidean space. We prove several jet-interpolation results for nowhere degenerate entire mappings F:Cn →Cnand for holomorphic automorphisms ofCnon

Noncritical holomorphic functions on Stein manifolds

We prove that every Stein manifold X of dimension n admits [(n+1)/2] holomorphic functions with pointwise independent differentials, and this number is maximal for every n. In particular, X admits a

The density property for complex manifolds and geometric structures

Definition Let g be a Lie algebra of holomorphic vector fields. We say that g has the density property if the Lie subalgebra of g generated by the complete vector fields in g is dense in g. When the

Optimality for totally real immersions and independent mappings of manifolds into C^N

The optimal target dimensions are determined for totally real immersions and for independent mappings into complex affine spaces. Our arguments are similar to those given by Forster, but we use

Stability of polynomial convexity of totally real sets

We show that certain compact polynomially convex subsets of C' remain polynomially convex under sufficiently small C2 perturbations. 1. Statement of the results. Let M be a Stein manifold. Denote by

Stein Manifolds and Holomorphic Mappings: The Homotopy Principle in Complex Analysis

Preliminaries. - Stein Manifolds. - Stein Neighborhoods and Holomorphic Approximation. - Automorphisms of Complex Euclidean Spaces. - Oka Manifolds. - Elliptic Complex Geometry and Oka Principle. -


In this paper I give a completed topological characterization of Stein manifolds of complex dimension >2. Another paper (see [E14]) is devoted to new topogical obstructions for the existence of a

Proper holomorphic embeddings into stein manifolds with the density property

We prove that a Stein manifold of dimension d admits a proper holomorphic embedding into any Stein manifold of dimension at least 2d + 1 satisfying the holomorphic density property. This generalizes