TY - JOUR A1 - Lauf, Wolfgang A1 - Schmieder, G. A1 - Volynec, I. A. T1 - The automorphism space Σ(G) of a domain without punctiform prime ends JF - The Journal of Geometric Analysis N2 - 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. KW - automorphism group KW - boundary behavior KW - complex approximation KW - conformal mapping KW - connectedness KW - total disconnectedness KW - prime ends Y1 - 2000 U6 - https://doi.org/10.1007/BF02921993 SN - 1050-6926 VL - 10 IS - 4 SP - 697 EP - 712 PB - Springer ER -