Displaying similar documents to “On the uniformization of Hartogs domains in ℂ 2 and their envelopes of holomorphy”

On ∂̅-problems on (pseudo)-convex domains

R. Range (1995)

Banach Center Publications

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In this survey we shall tour the area of multidimensional complex analysis which centers around ∂̅-problems (i.e., the Cauchy-Riemann equations) on pseudoconvex domains. Along the way we shall highlight some of the classical milestones as well as more recent landmarks, and we shall discuss some of the major open problems and conjectures. For the sake of simplicity we will only consider domains in ℂ n ; intriguing phenomena occur already in the simple setting of (Euclidean) convex domains....

On balanced L²-domains of holomorphy

Marek Jarnicki, Peter Pflug (1996)

Annales Polonici Mathematici

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We show that any bounded balanced domain of holomorphy is an L ² h -domain of holomorphy.

Embedding subsets of tori Properly into ℂ 2

Erlend Fornæss Wold (2007)

Annales de l’institut Fourier

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Let 𝕋 be a complex one-dimensional torus. We prove that all subsets of 𝕋 with finitely many boundary components (none of them being points) embed properly into ℂ 2 . We also show that the algebras of analytic functions on certain countably connected subsets of closed Riemann surfaces are doubly generated.

Hölder continuity of proper holomorphic mappings

François Berteloot (1991)

Studia Mathematica

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We prove the Hölder continuity for proper holomorphic mappings onto certain piecewise smooth pseudoconvex domains with "good" plurisubharmonic peak functions at each point of their boundaries. We directly obtain a quite precise estimate for the exponent from an attraction property for analytic disks. Moreover, this way does not require any consideration of infinitesimal metric.

Proper holomorphic mappings vs. peak points and Shilov boundary

Łukasz Kosiński, Włodzimierz Zwonek (2013)

Annales Polonici Mathematici

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We present a result on the existence of some kind of peak functions for ℂ-convex domains and for the symmetrized polydisc. Then we apply the latter result to show the equivariance of the set of peak points for A(D) under proper holomorphic mappings. Additionally, we present a description of the set of peak points in the class of bounded pseudoconvex Reinhardt domains.

Trivial generators for nontrivial fibres

Linus Carlsson (2008)

Mathematica Bohemica

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Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in ℂ n where the fibre is nontrivial, has to exceed n . This is shown not to be the case.