Riemann surfaces in Stein manifolds with the Density property

Rafael B. Andrist[1]; Erlend Fornæss Wold[2]

  • [1] Bergische Universität Wuppertal, Fachbereich C - Mathematik und Naturwissenschaften, Gaußstraße 20, 42119 Wuppertal, Germany
  • [2] Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 2, page 681-697
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Andrist, Rafael B., and Wold, Erlend Fornæss. "Riemann surfaces in Stein manifolds with the Density property." Annales de l’institut Fourier 64.2 (2014): 681-697. <http://eudml.org/doc/275619>.

@article{Andrist2014,
abstract = {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.},
affiliation = {Bergische Universität Wuppertal, Fachbereich C - Mathematik und Naturwissenschaften, Gaußstraße 20, 42119 Wuppertal, Germany; Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway},
author = {Andrist, Rafael B., Wold, Erlend Fornæss},
journal = {Annales de l’institut Fourier},
keywords = {Riemann surface; Stein manifold; proper holomorphic map; Andersen-Lempert theory; Density property; Volume Density property; density property; volume density property},
language = {eng},
number = {2},
pages = {681-697},
publisher = {Association des Annales de l’institut Fourier},
title = {Riemann surfaces in Stein manifolds with the Density property},
url = {http://eudml.org/doc/275619},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Andrist, Rafael B.
AU - Wold, Erlend Fornæss
TI - Riemann surfaces in Stein manifolds with the Density property
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 2
SP - 681
EP - 697
AB - 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.
LA - eng
KW - Riemann surface; Stein manifold; proper holomorphic map; Andersen-Lempert theory; Density property; Volume Density property; density property; volume density property
UR - http://eudml.org/doc/275619
ER -

References

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