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Let a and m be positive integers such that 2a < m. We show that in the domain $D : = {z \in ℂ ³ | r (z) : = ℜ z ₁ + | z ₁ | ² + | z ₂ |}^{2 m} + {| z ₂ z ₃ |}^{2 a} + {| z ₃ |}^{2 m} < 0$ the holomorphic sectional curvature $R_{D} (z; X)$ of the Bergman metric at z in direction X tends to -∞ when z tends to 0 non-tangentially, and the direction X is suitably chosen. It seems that an example with this feature has not been known so far.

An integral formula on submanifolds of domains of Cn..

Telemachos Hatziafratis (1991)

Publicacions Matemàtiques

A Bochner-Martinelli-Koppelman type integral formula on submanifolds of pseudoconvex domains in Cn is derived; the result gives, in particular, integral formulas on Stein manifolds.

An open mapping theorem for analytic multifunctions

Zbigniew Słodkowski (1997)

Studia Mathematica

The paper gives sufficient conditions for projections of certain pseudoconcave sets to be open. More specifically, it is shown that the range of an analytic set-valued function whose values are simply connected planar continua is open, provided there does not exist a point which belongs to boundaries of all the fibers. The main tool is a theorem on existence of analytic discs in certain polynomially convex hulls, obtained earlier by the author.

Analycity of CR Equivalences Between Some Real Hypersurfaces in ...n with Degenerate Levi Forms.

C.K. Han (1983)

Inventiones mathematicae

Analytic functionals and Bergman spaces

Paul Zorn (1982)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Analyticité globale pour ${\bar{\partial}}_{b}$ sur certaines hypersurfaces compactes de $ℂ^{n}$

Isabelle Reizner (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Analyticité semi-globale pour le $\bar{\partial}$ -Neumann dans des domaines pseudoconvexes

Benoît Ben Moussa (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Aneurysms of pseudoconcave CR manifolds.

C. Denson Hill, Mauro Nacinovich (1995)

Mathematische Zeitschrift

Application des techniques $L^{2}$ à la théorie des idéaux d’une algèbre de fonctions holomorphes avec poids

Henri Skoda (1972)

Annales scientifiques de l'École Normale Supérieure

Applications holomorphes de domaines disqués non bornés.

Jean-Jacques Loeb (2006)

Publicacions Matemàtiques

We give several extensions to unbounded domains of the following classical theorem of H. Cartan: A biholomorphism between two bounded complete circular domains of Cn which fixes the origin is a linear map. In our paper, pseudo-convexity plays a main role. Some precise study is done for the case of dimension two and the case where one of the domains is Cn.

Approximation by Holomorphic Functions on Pseudokonvex Domains with Isolated Degeneracies.

R. Michael Range (1977)

Manuscripta mathematica

Approximation d'operateurs d'extension minimale et de division.

Anne Cumenge, Pierre Bonneau (1991)

Mathematische Zeitschrift

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