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Some properties of Reinhardt domains

Le Mau Hai, Nguyen Quang Dieu, Nguyen Huu Tuyen (2003)

Annales Polonici Mathematici

We first establish the equivalence between hyperconvexity of a fat bounded Reinhardt domain and the existence of a Stein neighbourhood basis of its closure. Next, we give a necessary and sufficient condition on a bounded Reinhardt domain D so that every holomorphic mapping from the punctured disk Δ * into D can be extended holomorphically to a map from Δ into D.

Steinness of bundles with fiber a Reinhardt bounded domain

Karl Oeljeklaus, Dan Zaffran (2006)

Bulletin de la Société Mathématique de France

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 ).

Sur la transformation de Fourier-Laurent dans un groupe analytique complexe réductif

Michel Lassalle (1978)

Annales de l'institut Fourier

Soit H un groupe analytique compact : son complexifié universel G est un groupe analytique complexe réductif. On introduit dans G une classe de “domaines de Reinhardt généralisés”, bi-invariants par H et caractérisés par une “base”, définie dans une sous-algèbre abélienne maximale de l’algèbre de Lie du groupe H et invariante par le groupe de Weyl.On donne une caractérisation par leurs coefficients de Fourier-Laurent des fonctions holomorphes dans un tel domaine. On montre que l’enveloppe d’holomorphie...

The Bloch space for the minimal ball

G. Mengotti (2001)

Studia Mathematica

We introduce the Bloch space for the minimal ball and we prove that this space can be identified with the dual of a certain analytic space which is strongly related to the Bergman theory on the minimal ball.

The extended future tube conjecture for SO(1, 𝑛 )

Peter Heinzner, Patrick Schützdeller (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let C be the open upper light cone in ℝ 1 + n with respect to the Lorentz product. The connected linear Lorentz group SO ℝ ( 1 , n ) 0 acts on C and therefore diagonally on the N -fold product T N where T = ℝ 1 + n + i C ⊂ ℂ 1 + n . We prove that the extended future tube SO ℂ ( 1 , n ) · T N is a domain of holomorphy.

The holomorphic automorphism groups of twisted Fock-Bargmann-Hartogs domains

Hyeseon Kim, Atsushi Yamamori (2018)

Czechoslovak Mathematical Journal

We consider a certain class of unbounded nonhyperbolic Reinhardt domains which is called the twisted Fock-Bargmann-Hartogs domains. By showing Cartan's linearity theorem for our unbounded nonhyperbolic domains, we give a complete description of the automorphism groups of twisted Fock-Bargmann-Hartogs domains.

The Serre problem with Reinhardt fibers

Peter Pflug, Wlodzimierz Zwonek (2004)

Annales de l’institut Fourier

The Serre problem is solved for fiber bundles whose fibers are two-dimensional pseudoconvex hyperbolic Reinhardt domains.

Currently displaying 141 – 160 of 205