Embedding subsets of tori Properly into \mathbb{C}^2

Wold, Erlend Fornaess

doi:10.5802/aif.2305

Cited by 13 publications

(11 citation statements)

References 10 publications

(19 reference statements)

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“…Considerably more general results were obtained by the second author in recent papers [48,49,50]. In [49], Corollary 1.2 was proved under the additional assumption that each boundary curve C j of the image Σ = f (D) contains an exposed point p j = (p 1 j , p 2 j ), meaning that the vertical line {p 1 j }× C intersects the curve Σ only at p j and the intersection is transverse.…”

Section: Introductionmentioning

confidence: 89%

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Bordered Riemann surfaces in C^2

Forstneric,

Wold

2007

Preprint

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We prove that the interior of any compact complex curve with smooth boundary in C 2 admits a proper holomorphic embedding into C 2 . In particular, if D is a bordered Riemann surface whose closure admits a holomorphic embedding into C 2 , then D admits a proper holomorphic embedding into C 2 . R ÉSUM ÉOn montre que l'interieur d'une courbe complexe compacte avec bord lisse dans C 2 admet un plongement holomorphe propre dans C 2 . En particulier, si D est une surface de Riemann avec bord dont la fermeture admet un plongement holomorphe dans C 2 , alors D admet un plongement holomorphe propre dans C 2 .To Edgar Lee Stout on the occasion of his 70th birthday

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Section: Introductionmentioning

confidence: 89%

“…A main difference between our construction in this paper and those of Globevnik and Stensønes [27] (for planar domains) and Wold [50] (for domains in tori) is that the conformal structure on D does not change during the construction, and hence we do not need the uniformization theory in order to complete the proof.…”

Section: Introductionmentioning

confidence: 99%

Bordered Riemann surfaces in C^2

Forstneric,

Wold

2007

Preprint

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“…A new method based on Andersén-Lempert theory was introduced into the subject a decade later by Wold [179,178,180]. Assume that M is a compact bordered Riemann surface (every such is conformally equivalent to a domain in a compact Riemann surface obtained by removing finitely many pairwise disjoint discs [168,Theorem 8.1]) and F : M → C 2 is a smooth embedding which is holomorphic on M .…”

Section: Embedding Open Riemann Surfaces In Cmentioning

confidence: 99%

The first thirty years of Andersen-Lempert theory

Forstnerič¹,

Kutzschebauch²

2021

Preprint

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In this paper we expose the impact of the fundamental discovery, made by Erik Andersén and László Lempert in 1992, that the group generated by shears is dense in the group of holomorphic automorphisms of a complex Euclidean space of dimensions n > 1. In three decades since its publication, their groundbreaking work led to the discovery of several new phenomena and to major new results in complex analysis and geometry involving Stein manifolds and affine algebraic manifolds with many automorphisms. The aim of this survey is to present the focal points of these developments, with a view towards the future. Dedicated to LászlóLempert in honour of his 70th birthday CONTENTS 1. Introduction 2. Stein manifolds with density properties 2.1. Density property 2.2. Volume density property 2.3. Relative density properties 2.4. Fibred density properties 2.5. Symplectic density property 3. Automorphisms with given jets 4. Fatou-Bieberbach domains 5. Twisted complex lines in C n and nonlinearizable automorphisms 6. Embedding open Riemann surfaces in C 2 7. Complex manifolds exhausted by Euclidean spaces 8. Stein manifolds with the density property and Oka manifolds 9. Complete complex submanifolds 10. An application in 3-dimensional topology 11. The recognition problem for complex Euclidean spaces References

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“…The proof relies on techniques introduced mainly by Wold [106,105,107]. One of them concerns exposing boundary points of an embedded bordered Riemann surface in C 2 .…”

Section: 3mentioning

confidence: 99%

Holomorphic Embeddings and Immersions of Stein Manifolds: A Survey

Forstnerič

2018

Springer Proceedings in Mathematics &Amp; Statistics

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In this paper we survey results on the existence of holomorphic embeddings and immersions of Stein manifolds into complex manifolds. Most of them pertain to proper maps into Stein manifolds. We include a new result saying that every continuous map X → Y between Stein manifolds is homotopic to a proper holomorphic embedding provided that dim Y > 2 dim X and we allow a homotopic deformation of the Stein structure on X.

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Embedding subsets of tori Properly into \mathbb{C}^2

Cited by 13 publications

References 10 publications

Bordered Riemann surfaces in C^2

Bordered Riemann surfaces in C^2

The first thirty years of Andersen-Lempert theory

Holomorphic Embeddings and Immersions of Stein Manifolds: A Survey

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