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

Giorgio Patrizio (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Giorgio Patrizio (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Blank, Brian E., Fan, Dashan, Klein, David, Krantz, Steven G., Ma, Daowei, Pang, Myung-Yull (1992)

Experimental Mathematics

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Sergio Venturini (1989)

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

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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.

Sergio Venturini (1989)

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

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Prachi Mahajan (2012)

Annales Polonici Mathematici

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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...

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.

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.

Marius Overholt (1995)

Annales Polonici Mathematici

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The pseudometric of Hahn is identical to the Kobayashi-Royden pseudometric on domains of dimension greater than two. Thus injective hyperbolicity coincides with ordinary hyperbolicity in this case.

Gilberto Dini, Angela Selvaggi Primicerio (1988)

Rendiconti del Seminario Matematico della Università di Padova

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Nikolai Nikolov

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Łukasz Kosiński (2007)

Annales Polonici Mathematici

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A complete characterization of proper holomorphic mappings between domains from the class of all pseudoconvex Reinhardt domains in ℂ² with the logarithmic image equal to a strip or a half-plane is given.

Krantz, Steven G. (2010)

International Journal of Mathematics and Mathematical Sciences

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Budzyńska, Monika (2003)

Abstract and Applied Analysis

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Łukasz Kosiński (2009)

Annales Polonici Mathematici

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Lev Aizenberg (2007)

Studia Mathematica

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The Bohr radius for power series of holomorphic functions mapping Reinhardt domains 𝓓 ⊂ ℂⁿ into a convex domain G ⊂ ℂ is independent of the domain G.

Nabil Ourimi (2005)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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