Generalized stretch lines for surfaces with boundary


In 1986 William P. Thurston introduced the celebrated (asymmetric) Lipschitz distance on the Teichmueller space of a (closed or punctured) surface. In this paper we extend his work to the Teichmueller space of a surface with boundary endowed the arc distance. In this new setting we construct a large family of geodesics, which generalize Thurston’s stretch lines. We prove that the Teichmueller space of a surface with boundary, endowed with the arc distance, is a geodesic metric space. Furthermore, the arc distance is induced by a Finsler metric. As a corollary, we describe a new class of geodesics in the Teichmueller space of a closed/punctured surface that are not stretch lines in the sense of Thurston.


Research Groups: Groups and Geometry

Publication type: Misc

Journal: arXiv,math.GT,1911.10431

Citation: arXiv,math.GT,1911.10431

Date Published: 2019


Registered Mode: imported from a bibtex file

Authors: Daniele Alessandrini, Valentina Disarlo

help Submitter

Views: 5154

Created: 30th Jan 2020 at 10:36

Last updated: 5th Mar 2024 at 21:24

help Tags

This item has not yet been tagged.

help Attributions


Powered by
Copyright © 2008 - 2023 The University of Manchester and HITS gGmbH