Tautness and Complete Hyperbolicity of Domains in C

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.

Cite this paper

@inproceedings{GAUSSIER1998TautnessAC, title={Tautness and Complete Hyperbolicity of Domains in C}, author={HERV{\'E} GAUSSIER and Theodore W. Gamelin and Bernard Coupet and François Berteloot and J Rosay}, year={1998} }