@article{LaufSchmiederVolynec, author = {Lauf, Wolfgang and Schmieder, G. and Volynec, I. A.}, title = {The automorphism space Σ(G) of a domain without punctiform prime ends}, series = {The Journal of Geometric Analysis}, volume = {10}, journal = {The Journal of Geometric Analysis}, number = {4}, publisher = {Springer}, issn = {1050-6926}, doi = {10.1007/BF02921993}, pages = {697 -- 712}, abstract = {Let G ⊆ ℂ be a simply connected domain and let Σ (G) be its group of conformal automorphisms with the topology of uniform chordal convergence on G. In 1984 Gaier raised the question whether the connectedness of the space Σ (G) implies that the domain G has only punctiform prime ends. As a contribution to answering this question in this paper the authors use suitable spike Junctions to construct a bounded domain without any punctiform prime end such that its automorphism space Σ (G) is not discrete, but totally disconnected.}, language = {en} }