Displaying similar documents to “Riemann surfaces in Stein manifolds with the Density property”

On nonimbeddability of Hartogs figures into complex manifolds

E. Chirka, S. Ivashkovich (2006)

Bulletin de la Société Mathématique de France

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We prove the impossibility of imbeddings of Hartogs figures into general complex manifolds which are close to an imbedding of an analytic disc attached to a totally real collar. Analogously we provide examples of the so called thin Hartogs figures in complex manifolds having no neighborhood biholomorphic to an open set in a Stein manifold.

Oka manifolds: From Oka to Stein and back

Franc Forstnerič (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989. In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent...

Survey of Oka theory.

Forstnerič, Franc, Lárusson, Finnur (2011)

The New York Journal of Mathematics [electronic only]

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Terrence Napier, Mohan Ramachandran (0)

Annales de l’institut Fourier

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A Cartan-type result for invariant distances and one-dimensional holomorphic retracts.

Colum Watt (2001)

Publicacions Matemàtiques

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We derive conditions under which a holomorphic mapping of a taut Riemann surface must be an automorphism. This is an analogue involving invariant distances of a result of H. Cartan. Using similar methods we prove an existence result for 1-dimensional holomorphic retracts in a taut complex manifold.

Group-theoretic conditions under which closed aspherical manifolds are covered by Euclidean space

Hanspeter Fischer, David G. Wright (2003)

Fundamenta Mathematicae

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Hass, Rubinstein, and Scott showed that every closed aspherical (irreducible) 3-manifold whose fundamental group contains the fundamental group of a closed aspherical surface, is covered by Euclidean space. This theorem does not generalize to higher dimensions. However, we provide geometric tools with which variations of this theorem can be proved in all dimensions.