On various Teichmüller spaces of a surface of infinite topological type

Athanase Papadopoulos (1) , Daniele Alessandrini (1) , Lixin Liu (2) , Weixu Su (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Department of Mathematics

We show that the length spectrum metric on Teichmüller spaces of surfaces of infinite topological type is complete. We also give related results and examples that compare the length spectrum Teichm\üller space with quasiconformal and the Fenchel-Nielsen Teichmüller spaces on such surfaces

Mots clés: Surfaces of infinite topological type; Teichmüller space; Teichmüller metric; Quasiconformal metric; Length spectrum metric; Fenchel-Nielsen coordinates; Fenchel-Nielsen metric

Domaines: Topologie géométrique [math.GT]

Athanase Papadopoulos, Daniele Alessandrini, Lixin Liu, Weixu Su. On various Teichmüller spaces of a surface of infinite topological type. Proceedings of the American Mathematical Society, 2012, 140, pp.561-574. ⟨10.1090/S0002-9939-2011-10918-3⟩. ⟨hal-00507878⟩