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Displaying 1 – 20 of 166

A Cartan-type result for invariant distances and one-dimensional holomorphic retracts.

Colum Watt (2001)

Publicacions Matemàtiques

We derive conditions under which a holomorphic mapping of a taut Riemann surface must be an automorphism. This is an analogue involving invariant distances of a result of H. Cartan. Using similar methods we prove an existence result for 1-dimensional holomorphic retracts in a taut complex manifold.

A Characterization of the Ball by its Intrinsic Metrics.

Charles M. Stanton (1983)

Mathematische Annalen

A Characterization of the Polydisc.

Charles M. Stanton (1980)

Mathematische Annalen

A construction of hyperbolic hypersurface of P... ( C ).

Junjiro Noguchi, Kazuo Masuda (1996)

Mathematische Annalen

A Generalisation of a Theorem of Fornaess-Sibony.

Mechthild Behrens (1985/1986)

Mathematische Annalen

A generalization of Pick's theorem and its applications to intrinsic metrics

Jacob Burbea (1981)

Annales Polonici Mathematici

A generalized area integral estimate and applications

S. Chang (1981)

Studia Mathematica

A new invariant Kähler metric on relatively compact domains in a complex manifold

Bo-Yong Chen (2007)

Annales Polonici Mathematici

We introduce a new invariant Kähler metric on relatively compact domains in a complex manifold, which is the Bergman metric of the L² space of holomorphic sections of the pluricanonical bundle equipped with the Hermitian metric introduced by Narasimhan-Simha.

A note on Costara's paper

Armen Edigarian (2004)

Annales Polonici Mathematici

We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.

A note on the Kobayashi pseudodistance and the tautness of holomorphic fiber bundles

Do Duc Thai, Nguyen Le Huong (1993)

Annales Polonici Mathematici

We show a relation between the Kobayashi pseudodistance of a holomorphic fiber bundle and the Kobayashi pseudodistance of its base. Moreover, we prove that a holomorphic fiber bundle is taut iff both the fiber and the base are taut.

A notion of extremal analytic discs related to interpolation in the ball.

Eric Amar, Pascal J. Thomas (1994)

Mathematische Annalen

A propos de revêtements ramifiés d'espaces de Stein.

P. Le Barz (1976)

Mathematische Annalen

A special version of the Schwarz lemma on an infinite dimensional domain

Tatsuhiro Honda (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $B$ be the open unit ball of a Banach space $E$ , and let $f : B \to B$ be a holomorphic map with $f (0) = 0$ . In this paper, we discuss a condition whereby $f$ is a linear isometry on $E$ .

Almost Properness of Extremal Mappings

Armen Edigarian, Przemysław Kliś (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We give a simple proof of almost properness of any extremal mapping in the sense of Lempert function or in the sense of Kobayashi-Royden pseudometric.

An angle metric through the notion of Grassmann representative.

Kalogeropoulos, Grigoris I., Karageorgos, Athanasios D., Pantelous, Athanasios A. (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

An example of a pseudoconvex domain whose holomorphic sectional curvature of the Bergman metric is unbounded

Gregor Herbort (2007)

Annales Polonici Mathematici

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.

Analytic discs method in complex analysis [Book]

Armen Edigarian (2002)

Balls defined by nonsmooth vector fields and the Poincaré inequality

Annamaria Montanari, Daniele Morbidelli (2004)

Annales de l’institut Fourier

We provide a structure theorem for Carnot-Carathéodory balls defined by a family of Lipschitz continuous vector fields. From this result a proof of Poincaré inequality follows.

Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in $C^{n}$ with real analytic boundary

Andrea Iannuzzi (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

It is shown that given a bounded strictly convex domain $Ω$ in $C^{n}$ with real analitic boundary and a point $x_{0}$ in $Ω$ , there exists a larger bounded strictly convex domain $Ω^{'}$ with real analitic boundary, close as wished to $Ω$ , such that $Ω$ is a ball for the Kobayashi distance of $Ω^{'}$ with center $x_{0}$ . The result is applied to prove that if $Ω$ is not biholomorphic to the ball then any automorphism of $Ω$ extends to an automorphism of $Ω^{'}$ .

Behavior of invariant metrics near convexifiable boundary points

Nikolai Nikolov (2003)

Czechoslovak Mathematical Journal

The behaviour of the Carathéodory, Kobayashi and Azukawa metrics near convex boundary points of domains in $ℂ^{n}$ is studied.

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