On the inclusion of the quasiconformal Teichmüller space into the length-spectrum Teichmüller space

• Verfasst von: Alessandrini, Daniele [VerfasserIn]
• Titel: On the inclusion of the quasiconformal Teichmüller space into the length-spectrum Teichmüller space
• Verf.angabe: D. Alessandrini, L. Liu, A. Papadopoulos, W. Su
• Umfang: 25 S.
• Fussnoten: Published online: 29 August 2015 ; Gesehen am 09.02.2018
• Titel Quelle: Enthalten in: Monatshefte für Mathematik
• Jahr Quelle: 2016
• Band/Heft Quelle: 179(2016), 2, S. 165-189
• ISSN Quelle: 1436-5081
• DOI: doi:10.1007/s00605-015-0813-9
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1569364435

Abstract

This paper is about surfaces of infinite topological type. Unlike the case of surfaces of finite type, there are several deformation spaces associated with a surface S of infinite topological type. Such spaces depend on the choice of a basepoint (that is, the choice of a fixed conformal structure or hyperbolic structure on S) and they also depend on the choice of a distance on the set of equivalence classes of marked hyperbolic structures. We address the question of the comparison between two deformation spaces, namely, the quasiconformal Teichmüller space and the length-spectrum Teichmüller space. There is a natural inclusion map of the quasiconformal space into the length-spectrum space, which is not always surjective. We work under the hypothesis that the basepoint (a hyperbolic surface) satisfies a condition we call “upper-boundedness”. This means that this surface admits a pants decomposition defined by curves whose lengths are bounded above.