The first thirty years of Andersén-Lempert theory (Q2151138)

scientific article; zbMATH DE number 7551284

Language	Label	Description	Also known as
English	The first thirty years of Andersén-Lempert theory	scientific article; zbMATH DE number 7551284

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instance of

scholarly article

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title

The first thirty years of Andersén-Lempert theory (English)

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30 June 2022

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full work available at URL

https://arxiv.org/abs/2111.08802

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zbMATH Keywords

holomorphic automorphism

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complete vector field

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density property

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Complete complex hypersurfaces in the ball come in foliations

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Every bordered Riemann surface is a complete proper curve in a ball

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Complete densely embedded complex lines in ℂ²

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A foliation of the ball by complete holomorphic discs

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Minimal Surfaces from a Complex Analytic Viewpoint

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Complete embedded complex curves in the ball of $\mathbb{C}^2$ can have any topology

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A construction of complete complex hypersurfaces in the ball with control on the topology

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Complete bounded embedded complex curves in $\mathbb {C}^2$

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Volume-preserving automorphisms of C⊃n⊃

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Complete vector fields on (ℂ*)ⁿ

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On the group of holomorphic automorphisms of $\mathbb{C}{}^ n$

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Stein spaces characterized by their endomorphisms

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The density property for Gizatullin surfaces with reduced degenerate fibre

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The density property for Calogero–Moser spaces

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Proper holomorphic embeddings into Stein manifolds with the density property

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Varieties characterized by their endomorphisms

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The fibred density property and the automorphism group of the spectral ball

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The density property for Gizatullin surfaces completed by four rational curves

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A new notion of tameness

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Riemann surfaces in Stein manifolds with the density property

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Chaotic holomorphic automorphisms of Stein manifolds with the volume density property

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Generic aspects of holomorphic dynamics on highly flexible complex manifolds

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Flexible varieties and automorphism groups

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Knotted holomorphic discs in

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Q3981482

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Polynomial Diffeomorphisms of C 2 . II: Stable Manifolds and Recurrence

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Zur Theorie der Funktionen mehrerer komplexer Veränderlichen. Über die Verallgemeinerung des Weierstrass'schen Produktsatzes

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Q3360475

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Mappings of Partially Analytic Spaces

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A long $\mathbb{C}^2$ without holomorphic functions

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Q5800951

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NON-EQUIVALENT EMBEDDINGS INTO COMPLEX EUCLIDEAN SPACES

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Automorphisms of $\mathbb C^k$ with an invariant non-recurrent attracting Fatou component biholomorphic to $\mathbb C \times (\mathbb C^\ast)^{k-1}$

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On the hyperbolicity of general hypersurfaces

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Q4884466

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An embedding of $\mathbb C$ in $\mathbb C^2$ with hyperbolic complement

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A Carleman type theorem for proper holomorphic embeddings

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An interpolation theorem for holomorphic automorphisms of ${\mathbb{C}}^n$

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A Fatou-Bieberbach domain avoiding a neighborhood of a variety of codimension 2

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Embedding some bordered Riemann surfaces in the affine plane

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On holomorphic embedding of planar domains into $\mathbb{C}^2$

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Construction of labyrinths in pseudoconvex domains

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Real hypersurfaces in complex manifolds

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New examples of Stein manifolds with volume density property

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Nonlinearizable holomorphic group actions

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Michael’s problem and the Poincaré-Fatou-Bieberbach phenomenon

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Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten

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Algebraic density property of Danilov-Gizatullin surfaces

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Complete proper holomorphic embeddings of strictly pseudoconvex domains into balls

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Strongly pseudoconvex domains as subvarieties of complex manifolds

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Inequivalent embeddings of the Koras-Russell cubic 3-fold

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Automorphism Groups of Certain Rational Hypersurfaces in Complex Four-Space

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Embeddings of Stein manifolds of dimension $n$ into the affine space of dimension $3n/2+1$

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On complex affine surfaces with $\mathbb{C}^ +$-action

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An increasing sequence of Stein manifolds whose limit is not Stein

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Q4663769

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Increasing sequences of complex manifolds

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Complex Hénon mappings in ${\mathbb{C}}^ 2$ and Fatou-Bieberbach domains

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The closing lemma for holomorphic maps

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STABLE MANIFOLDS OF HOLOMORPHIC HYPERBOLIC MAPS

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Spreading Polydiscs on Complex Manifolds

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Plongements des variétés de Stein

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Approximation by automorphisms on smooth submanifolds of $\mathbb{C}^ n$

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A theorem in complex symplectic geometry

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Actions of $(\mathbf R,+)$ and $(\mathbf C,+)$ on complex manifolds

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Interpolation by holomorphic automorphisms and embeddings in ${\mathbb{C}}^n$

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Noncritical holomorphic functions on Stein manifolds.

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Stein Manifolds and Holomorphic Mappings

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Holomorphic families of long $\mathbb{C}^{2}$'s

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Stein Manifolds and Holomorphic Mappings

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Holomorphic embeddings and immersions of Stein manifolds: a survey

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Proper holomorphic immersions into Stein manifolds with the density property

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Non straightenable complex lines in $\mathbb C^2$

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Oka properties of groups of holomorphic and algebraic automorphisms of complex affine space

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Oka's principle for holomorphic fiber bundles with sprays

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Oka properties of ball complements

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Approximation of biholomorphic mappings by automorphisms of $\mathbb{C}^ n$

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Bordered Riemann surfaces in $\mathbb C^2$

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Embeddings of infinitely connected planar domains into $\mathbb C^2$

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Fatou-Bieberbach domains in $\mathbb C^n\setminus\mathbb R^k$

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Holomorphic families of Fatou-Bieberbach domains and applications to Oka manifolds

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Runge tubes in Stein manifolds with the density property

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On Zariski problem

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Q5625343

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A bounded domain in $\mathbb{C}^N$ which embeds holomorphically into $\mathbb{C}^{N+1}$

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On Fatou-Bieberbach domains

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A complete complex hypersurface in the ball of $\mathbb{C}^N$

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Holomorphic functions unbounded on curves of finite length

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Holomorphic embeddings of planar domains in $\mathbb{C}^ 2$

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Theory of Stein spaces. Transl. from the German by Alan Huckleberry

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Partial Differential Relations

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Oka's Principle for Holomorphic Sections of Elliptic Bundles

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Fixed points, Koebe uniformization and circle packings

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Effective Actions of the Unitary Group on Complex Manifolds

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On the meromorphic function field of a Stein variety

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A Complete Bounded Complex Submanifold of C 3

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Extensions of isomorphisms of subvarieties in flexible varieties

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ℂ*-actions on ℂ³ are linearizable

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Criteria for the density property of complex manifolds

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Density property for hypersurfaces $UV = p({\overline X})$

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Algebraic volume density property of affine algebraic manifolds

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On the present state of the Andersen-Lempert theory

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On the Density and the Volume Density Property

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On algebraic volume density property

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Algebraic (volume) density property for affine homogeneous spaces

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Q4344786

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Affine modifications and affine hypersurfaces with a very transitive automorphism group

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Holomorphic mappings of polydiscs into compact complex manifolds

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Q3686804

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Automorphism groups of affine varieties and a characterization of affine $n$-space

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Oka complements of countable sets and nonelliptic Oka manifolds

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Elliptic characterization and localization of Oka manifolds

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ANDERSÉN–LEMPERT-THEORY WITH PARAMETERS: A REPRESENTATION THEORETIC POINT OF VIEW

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Manifolds with infinite dimensional group of holomorphic automorphisms and the Linearization Problem

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Sufficient conditions for holomorphic linearisation

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The algebraic density property for affine toric varieties

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Embedding some Riemann surfaces into ${\mathbb {C}^2}$ with interpolation

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Embedding Riemann surfaces with isolated punctures into the complex plane

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An Oka principle for a parametric infinite transitivity property

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A Characterization of Linearizability for Holomorphic ℂ*-Actions

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Carleman approximation by holomorphic automorphisms of $\mathbb{C}^n$

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(Volume) density property of a family of complex manifolds including the Koras-Russell cubic threefold

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Polynomial completion of symplectic jets and surfaces containing involutive lines

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Embedding certain infinitely connected subsets of bordered Riemann surfaces properly into $\mathbb C^{2}$

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Proper holomorphic embeddings of finitely connected planar domains into $\mathbb C^n$

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On the hypersurface $x+x^2y+z^2+t^3=0$ in $\mathbb{C}^4$ or a $\mathbb{C}^3$-like threefold which is not $\mathbb{C}^3$

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Affine surfaces containing cylinderlike open sets

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Automorphism groups of Koras-Russell threefolds of the first kind

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Imbedding of Holomorphically Complete Complex Spaces

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Automorphismes analytiques admettant des sous-variétés de points fixés attractives dans la direction transversale

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Applications holomorphes injectives de ${\mathbb{C}}^ 2$ dans lui-même qui exceptent une droite complex

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Q5772336

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ATTRACTING BASINS OF VOLUME PRESERVING AUTOMORPHISMS OF ℂk

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A topological characterisation of the affine plane as an algebraic variety

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Non-algebraic examples of manifolds with the volume density property

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Parametric jet interpolation for Stein manifolds with the density property

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Das Typenproblem bei formal-biholomorphen Abbildungen mit anziehendem Fixpunkt

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Normalformen biholomorpher Abbildungen mit anziehendem Fixpunkt

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Q3232434

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Holomorphic Maps from C n to C n

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Q4694618

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Injective Polynomial Maps are Automorphisms

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Q4847232

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Embeddings of Stein spaces into affine spaces of minimal dimension

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Q5529113

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Q3931547

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Q5657039

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Überlagerungen holomorph-vollständiger komplexer Räume

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Fatou-Bieberbach domains with $C^ \infty$-smooth boundary

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Local Contractions and a Theorem of Poincare

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The analytic part of the Runge hull

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Uniform approximation on smooth curves

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Bounded Holomorphic Functions on Finite Riemann Surfaces

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Propriétés topologiques des polynômes de deux variables complexes et automorphismes algébriques de l'espace $C^2$

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Holomorphic diffeomorphisms of complex semisimple Lie groups

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A parametric jet-interpolation theorem for holomorphic automorphisms of $\mathbb {C}^n$

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A general notion of shears, and applications

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THE DENSITY PROPERTY FOR COMPLEX MANIFOLDS AND GEOMETRIC STRUCTURES II

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The density property for complex manifolds and geometric structures

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An example concerning polynomial convexity

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TAME DISCRETE SUBSETS IN STEIN MANIFOLDS

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FATOU–BIEBERBACH DOMAINS

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EMBEDDING RIEMANN SURFACES PROPERLY INTO ℂ2

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Proper holomorphic embeddings of finitely and some infinitely connected subsets of $\mathbb C$ into $\mathbb C^2$

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Embedding subsets of tori properly into $\mathbb C^2$

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A Fatou-Bieberbach domain in $\mathbb C^2$ which is not Runge

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A long $\mathbb C^2$ which is not Stein

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A Fatou-Bieberbach domain intersecting the plane in the unit disk

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Q4127019

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Curvatures of complex submanifolds of $C^n$

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Integer homology 3-spheres admit irreducible representations in $\mathrm{SL}(2,{\mathbb C})$

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Identifiers

Mathematics Subject Classification ID

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10.1007/S10476-022-0130-1

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Sitelinks

Mathematics(1 entry)

mardi Publication:2151138