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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Tautness and complete hyperbolicity
of domains in $\mathbb C^n$


Author: Hervé Gaussier
Journal: Proc. Amer. Math. Soc. 127 (1999), 105-116
MSC (1991): Primary 32M99; Secondary 32M05, 32H05
DOI: https://doi.org/10.1090/S0002-9939-99-04492-5
MathSciNet review: 1458872
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Abstract: We prove that the existence of a local peak holomorphic function at each boundary point of an unbounded domain and at infinity implies the complete hyperbolicity of this domain, and we give a link between local tautness and global tautness of a domain. We end the note with some examples of taut and complete hyperbolic domains arising from the study of domains with noncompact automorphisms group.


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Additional Information

Hervé Gaussier
Affiliation: Centre de Mathematiques et Informatique, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France
Email: gaussier@gyptis.univ-mrs.fr

DOI: https://doi.org/10.1090/S0002-9939-99-04492-5
Received by editor(s): December 10, 1996
Received by editor(s) in revised form: April 30, 1997
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society