Stein domains in complex surfaces
type: Item
instance of: scholarly article
title: Stein domains in complex surfaces
zbMATH Open document ID: 1039.32013
DOI: 10.1007/BF02930998
author: Franc Forstnerič
published in: The Journal of Geometric Analysis
publication date: 2003-12-04T00:00:00Z
review text: Let \(S\) be a closed connected real surface and \(\pi : S \rightarrow X\) a smooth embedding or immersion of \(S\) into a complex surface \(X\). The author finds conditions (related to the number of complex points of \(\pi ( S ) \) in \( X)\) under which \(\pi\) can be \(C^{0}\) approximated by an isotopic immersion \(\pi_{1} : S \rightarrow X\) whose image has a basis of open Stein neighbourhoods in \(X\) which are homotopy equivalent to \(\pi_{1}(S)\). Some very interesting examples and precise results for \(\mathbb{C} P^{2}\) are presented. Open problems related to the subject are also given.
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32Q28
Mathematics Subject Classification ID: 32Q55
Mathematics Subject Classification ID: 32V40
zbMATH DE Number: 2013177
zbMATH Keywords: Stein domains
zbMATH Keywords: complex surfaces
zbMATH Keywords: adjunction inequalities
zbMATH Keywords: symplectic spheres
reviewed by: Eugen Pascu
MaRDI profile type: Publication
cites work: The Lefschetz theorem on hyperplane sections
cites work: Differentiable manifolds in complex Euclidean space
cites work: On the Envelope of Holomorphy of a 2-Sphere in ℂ 2
cites work: A theorem on orientable surfaces in four-dimensional space
cites work: Algebraic approximations of holomorphic maps from Stein domains to projective manifolds
cites work: TOPOLOGICAL CHARACTERIZATION OF STEIN MANIFOLDS OF DIMENSION >2
cites work: Q4716784
cites work: Analytic disks with boundaries in a maximal real submanifold of \({\mathbb C}^ 2\)
cites work: Complex tangents of real surfaces in complex surfaces
cites work: A new class of polynomially convex sets
cites work: Handlebody construction of Stein surfaces
cites work: Q4700561
cites work: On Levi's problem and the imbedding of real-analytic manifolds
cites work: Partial Differential Relations
cites work: Q4195061
cites work: Q4143433
cites work: Structure of the moduli space in a neighborhood of a cusp-curve and meromorphic hulls
cites work: Local polynomial hulls of discs near isolated parabolic points
cites work: The local hull of holomorphy of a surface in the space of two complex variables
cites work: The genus of embedded surfaces in the projective plane
cites work: Q3986332
cites work: Characteristic Classes of Real Manifolds Immersed in Complex Manifolds
cites work: Tight contact structures and Seiberg-Witten invariants
cites work: Q4865492
cites work: A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture
cites work: Complex analysis and differential topology on complex surfaces
cites work: The symplectic Thom conjecture
cites work: Shorter Notes: Totally Real Klein Bottles in C 2
cites work: Q3709082
cites work: The Seiberg-Witten invariants and symplectic forms
cites work: SW ⇒ Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves
cites work: Minimal surfaces in a Kähler surface
cites work: Q4192639
cites work: Local polynomially convex hulls at degenerated CR singularities of surfaces in C^2
cites work: Monopoles and four-manifolds
description: scientific article; zbMATH DE number 2013177