All plane domains are Banach-Stein

Siu, Yum Tong

doi:10.1007/bf01637626

Cited by 21 publications

(5 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stein [18] proved that if dim F = 0, then F ∈ S. Building on previous work by A. Hirschowitz [5], Y.T. Siu [13] and N. Sibony [12], N. Mok [7] proved that if dim F = 1, then F ∈ S. Skoda's above result can be stated as: C 2 ∈ S.…”

Section: Introduction and Notationsmentioning

confidence: 90%

Steinness of bundles with fiber a Reinhardt bounded domain

Oeljeklaus¹,

Zaffran

2006

Bul. Soc. Math. France

View full text Add to dashboard Cite

Abstract.-Let E denote a holomorphic bundle with fiber D and with basis B. Both D and B are assumed to be Stein. For D a Reinhardt bounded domain of dimension d = 2 or 3, we give a necessary and sufficient condition on D for the existence of a non-Stein such E (Theorem 1); for d = 2, we give necessary and sufficient criteria for E to be Stein (Theorem 2). For D a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for E to be Stein (Theorem 3).

show abstract

Section: Introduction and Notationsmentioning

confidence: 90%

Steinness of bundles with fiber a Reinhardt bounded domain

Oeljeklaus¹,

Zaffran

2006

Bul. Soc. Math. France

View full text Add to dashboard Cite

show abstract

“…Remark 1.2. Upon finishing a preprint of the current article we were made aware of the fact that the injective Kobayashi metric was already introduced in [3], and that it already appeared in the one-dimensional case in [11]. In [4] the corresponding object(s) are referred to as Hahn functions/metrics.…”

Section: Introductionmentioning

confidence: 99%

Injective Hyperbolicity for quotients of balls and polydisks

Fornaess,

Trybula,

Wold

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The answer is 'Yes' for n = 0 (Stein [23] and Le Barz [12]) and n = 1 (Mok [13]. In fact, some partial results were previously proved by various authors, Siu [19], Sibony [18], Hirschowitz [9], etc).…”

Section: §1 Introductionmentioning

confidence: 99%

Locally trivial fibrations with singular 1-dimensional Stein fiber over q-complete spaces

Colţoiu¹,

Vâjâitu²

2000

Nagoya Mathematical Journal

View full text Add to dashboard Cite

Abstract. In connection with Serre's problem, we consider a locally trivial analytic fibration π : E −→ B of complex spaces with typical fiber X. We show that if X is a Stein curve and B is q-complete, then E is q-complete. §1. Introduction Let π : E → B be a locally trivial analytic fibration of complex spaces with Stein fiber X of dimension n.The following question was raised by Serre [17]:Under the above assumptions, does it follow that E is Stein if B is Stein?The answer is 'Yes' for n = 0 Related to this circle of ideas we study the case when the base B is q-complete. The normalization is chosen such that Stein spaces correspond to 1-complete spaces.For n = 0, i.e., E is a topological covering of B, Ballico [2] proved the q-completeness of E. This is a particular case of a result due to Vâjâitu [24] which gives that if π : Y → Z is a locally trivial analytic fibration with hyperconvex fibre and Z is q-complete, then Y is q-complete. (A complex space S is said to be hyperconvex if S is Stein and has a negative exhaustion function which is continuous and plurisubharmonic.)For n = 1, in order to generalize Mok's result, Vâjâitu [26] showed if X is non-singular, E is q-complete if B is q-complete. It remained the open problem when X is a singular Stein curve.

show abstract

All plane domains are Banach-Stein

Cited by 21 publications

References 1 publication

Steinness of bundles with fiber a Reinhardt bounded domain

Steinness of bundles with fiber a Reinhardt bounded domain

Injective Hyperbolicity for quotients of balls and polydisks

Locally trivial fibrations with singular 1-dimensional Stein fiber over q-complete spaces

Contact Info

Product

Resources

About