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Displaying 101 – 120 of 166

On holomorphic isometries for the Kobayashi and Carathéodory distances on complex manifolds

Sergio Venturini (1989)

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

It is shown that under certain conditions every holomorphic isometry for the Carathéodory or the Kobayashi distances is an isometry for the corrisponding metrics. These results are used to give a characterization of biholomorphic mappings between convex domains and complete circular domains.

On holomorphic maps between domains in $C^{n}$

Giorgio Patrizio (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On horospheres and holomorphic endomorfisms of the Siegel disc

Giovanni Bassanelli (1983)

Rendiconti del Seminario Matematico della Università di Padova

On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains

Harish Seshadri (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $Ω_{1}$ and $Ω_{2}$ be $strongly pseudoconvex$ domains in $ℂ^{n}$ and $f : Ω_{1} \to Ω_{2}$ an isometry for the Kobayashi or Carathéodory metrics. Suppose that $f$ extends as a $C^{1}$ map to ${\bar{Ω}}_{1}$ . We then prove that ${f |}_{\partial Ω_{1}} : \partial Ω_{1} \to \partial Ω_{2}$ is a CR or anti-CR diffeomorphism. It follows that $Ω_{1}$ and $Ω_{2}$ must be biholomorphic or anti-biholomorphic.

On isometries of the Kobayashi and Carathéodory metrics

Prachi Mahajan (2012)

Annales Polonici Mathematici

This article considers C¹-smooth isometries of the Kobayashi and Carathéodory metrics on domains in ℂⁿ and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that 𝔹ⁿ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C⁰-isometries f : D₁ → D₂ to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C⁰-isometry between a strongly...

On iterates of holomorphic maps.

Daowei Ma (1991)

Mathematische Zeitschrift

On Lempert functions in $ℂ^{2}$ .

Jarnicki, Witold (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

On symmetry of the pluricomplex Green function for ellipsoids

Włodzimierz Zwonek (1997)

Annales Polonici Mathematici

We show that in the class of complex ellipsoids the symmetry of the pluricomplex Green function is equivalent to convexity of the ellipsoid.

On the Bergman distance on model domains in ℂⁿ

Gregor Herbort (2016)

Annales Polonici Mathematici

Let P be a real-valued and weighted homogeneous plurisubharmonic polynomial in $ℂ^{n - 1}$ and let D denote the “model domain” z ∈ ℂⁿ | r(z):= Re z₁ + P(z’) < 0. We prove a lower estimate on the Bergman distance of D if P is assumed to be strongly plurisubharmonic away from the coordinate axes.

On the Geodesics of the Bergman Metric.

Gregor Herbort (1983)

Mathematische Annalen

On the Geometry of Moduli Spaces.

Georg Schumacher (1985)

Manuscripta mathematica

On the Green function on a certain class of hyperconvex domains

Gregor Herbort (2008)

Annales Polonici Mathematici

We study the behavior of the pluricomplex Green function on a bounded hyperconvex domain D that admits a smooth plurisubharmonic exhaustion function ψ such that 1/|ψ| is integrable near the boundary of D, and moreover satisfies the estimate $| ψ | \leq C e x p (- C^{'} {(l o g (1 / δ_{D}))}^{α})$ at points close enough to the boundary with constants C,C’ > 0 and 0 < α < 1. Furthermore, we obtain a Hopf lemma for such a function ψ. Finally, we prove a lower bound on the Bergman distance on D.

On the Hausdorff measures associated to the Carathéodory and Kobayashi metrics

J. Bland, Ian Graham (1985)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On the Kähler form of the moduli space of once punctured tori.

Scott Wolpert (1983)

Commentarii mathematici Helvetici

On the Kobayashi and Caratheodory pseudometric reductions of homogeneous complex spaces

B. Gilligan (1986)

Matematički Vesnik

On the Kobayashi metric for perturbations of the ball.

Leslie D. Kay (1993)

Mathematische Zeitschrift

On the Kobayashi-Royden metric for ellipsoids.

L.D. Kay (1991)

Mathematische Annalen

On the product property of the Carathéodory pseudodistance

José M. Isidro, Jean-Pierre Vigué (2000)

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

We prove that, for certain domains $D$ , continuous product of domains $D_{ω}$ , the Carathéodory pseudodistance satisfies the following product property $C_{D} (f, g) = {sup}_{ω} C_{D_{ω}} (f (ω), g (ω))$

On the spectral Nevanlinna-Pick problem

Constantin Costara (2005)

Studia Mathematica

We give several characterizations of the symmetrized n-disc Gₙ which generalize to the case n ≥ 3 the characterizations of the symmetrized bidisc that were used in order to solve the two-point spectral Nevanlinna-Pick problem in ℳ ₂(ℂ). Using these characterizations of the symmetrized n-disc, which give necessary and sufficient conditions for an element to belong to Gₙ, we obtain necessary conditions of interpolation for the general spectral Nevanlinna-Pick problem. They also allow us to give a...

On the zero set of the Kobayashi-Royden pseudometric of the spectral unit ball

Nikolai Nikolov, Pascal J. Thomas (2008)

Annales Polonici Mathematici

Given A∈ Ωₙ, the n²-dimensional spectral unit ball, we show that if B is an n×n complex matrix, then B is a “generalized” tangent vector at A to an entire curve in Ωₙ if and only if B is in the tangent cone $C_{A}$ to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.

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