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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.
F. Berteloot, S. Pinchuk (1995)
Mathematische Zeitschrift
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Gilberto Dini, Angela Selvaggi Primicerio (1988)
Rendiconti del Seminario Matematico della Università di Padova
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Yifei Pan (1991)
Mathematische Zeitschrift
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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.
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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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.
P. Pflug, M. Jarnicki (1985)
Annales Polonici Mathematici
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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.
Bernard Coupet, Nabil Ourimi (2001)
Publicacions Matemàtiques
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We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in C. It appears, in particular, that it is controlled only by the first domain. As an application, we prove that proper holomorphic self-mappings between such domains are biholomorphic.
Krantz, Steven G. (2010)
International Journal of Mathematics and Mathematical Sciences
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Nabil Ourimi (2005)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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J.E. Fornaess, K. Diederich (1988)
Mathematische Annalen
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J.A. Cima, S.G. Krantz, T. Suffridge (1984)
Mathematische Zeitschrift
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Steven R. Bell (1982)
Commentarii mathematici Helvetici
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