Holomorphic Lipschitz functions and application to the -problem
Der-Chen Chang, Steven Krantz (1991)
Colloquium Mathematicae
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Der-Chen Chang, Steven Krantz (1991)
Colloquium Mathematicae
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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...
John Erik Fornaess, Edgar Lee Stout (1982)
Annales de l'institut Fourier
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Every -dimensional complex manifold (connected, paracompact and Hausdorff) is the image of the unit ball in under a finite holomorphic map that is locally biholomorphic.
Jianwen Zhang (1992)
Colloquium Mathematicae
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Giorgio Patrizio (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Le Mau Hai, Nguyen Quang Dieu, Nguyen Huu Tuyen (2003)
Annales Polonici Mathematici
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We first establish the equivalence between hyperconvexity of a fat bounded Reinhardt domain and the existence of a Stein neighbourhood basis of its closure. Next, we give a necessary and sufficient condition on a bounded Reinhardt domain D so that every holomorphic mapping from the punctured disk into D can be extended holomorphically to a map from Δ into D.
Alberto Scalari (1997)
Rendiconti del Seminario Matematico della Università di Padova
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Mats Andersson, Hasse Carlsson (1995)
Revista Matemática Iberoamericana
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Let D be a bounded strictly pseudoconvex domain in C. We construct approximative solution formulas for the equation i∂∂`u = θ, θ being an exact (1,1)-form in D. We show that our formulas give simple proofs of known estimates and indicate further applications.