Tautness and complete hyperbolicity of domains in ℂⁿ

Gaussier, Hervé

doi:10.1090/S0002-9939-99-04492-5

Tautness and complete hyperbolicity of domains in $\mathbb {C}^n$
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by Hervé Gaussier

Proc. Amer. Math. Soc. 127 (1999), 105-116

DOI: https://doi.org/10.1090/S0002-9939-99-04492-5

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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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