New examples of Stein manifolds with volume density property

Vito, Giorgio De

doi:10.1007/s40627-020-00043-y

Cited by 4 publications

(2 citation statements)

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“…have the volume density property for the unique algebraic volume form on them (De Vito [52]). Uniqueness of the algebraic volume form (up to a constant) again follows from simple connectedness of the manifolds.…”

Section: The List Of Examples Of Stein Manifolds Known To Have the Vo...mentioning

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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Section: The List Of Examples Of Stein Manifolds Known To Have the Vo...mentioning

confidence: 99%

The first thirty years of Andersen-Lempert theory

Forstnerič¹,

Kutzschebauch²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…They were the starting point for the introduction of the class of generalized Gizatullin surfaces whose final classification was achieved in [KKL20]. The topology of these fibers for any number of elementary factors has been studied in [DeVi20] where it was also proven that they admit the algebraic volume density property. Such studies are interesting since the possible topological types of Oka manifolds or manifolds with the density property are not understood at the moment.…”

Section: Product Of Exponentials and Open Questionsmentioning

confidence: 99%