On the continuous extension of holomorphic correspondences
F. Berteloot, A. Sukhov (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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F. Berteloot, A. Sukhov (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Nabil Ourimi (2003)
Publicacions Matemàtiques
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In this paper we prove some compactness theorems of families of proper holomorphic correspondences. In particular we extend the well known Wong-Rosay's theorem to proper holomorphic correspondences. This work generalizes some recent results proved in [17].
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.
Nabil Ourimi (2005)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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.
Krantz, Steven G. (2010)
International Journal of Mathematics and Mathematical Sciences
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Bernard Coupet (1993)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.