A boundary rigidity problem for holomorphic mappings.
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Gentili, Graziano, Migliorini, Serena (1997)
General Mathematics
W. Kucharz (1996)
Manuscripta mathematica
Yum-Tong Siu, Sai-Kee Yeung (1996)
Mathematische Annalen
Franc Forstneric (1993)
Mathematische Zeitschrift
Chiara Frosini, Fabio Vlacci (2007)
Annales Polonici Mathematici
In this survey we give geometric interpretations of some standard results on boundary behaviour of holomorphic self-maps in the unit disc of ℂ and generalize them to holomorphic self-maps of some particular domains of ℂⁿ.
J.E. Fornaess, G.T. Buzzard (1996)
Mathematische Annalen
Yasheng Ye, Xuecheng Pang, Liu Yang (2015)
Annales Polonici Mathematici
In this paper, the definition of the derivative of meromorphic functions is extended to holomorphic maps from a plane domain into the complex projective space. We then use it to study the normality criteria for families of holomorphic maps. The results obtained generalize and improve Schwick's theorem for normal families.
Jean-Jacques Loeb (2006)
Publicacions Matemàtiques
We give several extensions to unbounded domains of the following classical theorem of H. Cartan: A biholomorphism between two bounded complete circular domains of Cn which fixes the origin is a linear map. In our paper, pseudo-convexity plays a main role. Some precise study is done for the case of dimension two and the case where one of the domains is Cn.
Francine Meylan (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Let be a complex Banach space. Recall that admits afinite-dimensional Schauder decompositionif there exists a sequence of finite-dimensional subspaces of such that every has a unique representation of the form with for every The finite-dimensional Schauder decomposition is said to beunconditionalif, for every the series which represents converges unconditionally, that is, converges for every permutation of the integers. For short, we say that admits an unconditional F.D.D.We...
J. Bochnak, W. Kucharz (2003)
Annales Polonici Mathematici
Let X be a nonsingular complex algebraic curve and let Y be a nonsingular rational complex algebraic surface. Given a compact subset K of X, every holomorphic map from a neighborhood of K in X into Y can be approximated by rational maps from X into Y having no poles in K. If Y is a nonsingular projective complex surface with the first Betti number nonzero, then such an approximation is impossible.
Robert Juhlin, Bernhard Lamel (2013)
Journal of the European Mathematical Society
We show that the local automorphism group of a minimal real-analytic CR manifold is a finite dimensional Lie group if (and only if) is holomorphically nondegenerate by constructing a jet parametrization.
Róbert Szöke (1995)
Mathematische Zeitschrift
Alberto Farina, Berardino Sciunzi, Enrico Valdinoci (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
We use a Poincaré type formula and level set analysis to detect one-dimensional symmetry of stable solutions of possibly degenerate or singular elliptic equations of the formOur setting is very general and, as particular cases, we obtain new proofs of a conjecture of De Giorgi for phase transitions in and and of the Bernstein problem on the flatness of minimal area graphs in . A one-dimensional symmetry result in the half-space is also obtained as a byproduct of our analysis. Our approach...
Yifei Pan (1996)
Manuscripta mathematica
Larbi Belkhchicha (1994)
Mathematische Zeitschrift
Xiaojun Huang, Shanyu Ji (2002)
Annales de l’institut Fourier
For a strongly pseudoconvex domain defined by a real polynomial of degree , we prove that the Lie group can be identified with a constructible Nash algebraic smooth variety in the CR structure bundle of , and that the sum of its Betti numbers is bounded by a certain constant depending only on and . In case is simply connected, we further give an explicit but quite rough bound in terms of the dimension and the degree of the defining polynomial. Our approach is to adapt the Cartan-Chern-Moser...
Gabriela Kohr, Mirela Kohr (1997)
Annales Polonici Mathematici
We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in . Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain with p ≥ 1.
Filippo Bracci (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Jörg Winkelmann (1998)
Mémoires de la Société Mathématique de France
de Fabritiis, Ch. (2003)
Advances in Geometry
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