TY - JOUR
T1 - Generalizing Stretch Lines for Surfaces with Boundary
AU - Alessandrini, Daniele
AU - Disarlo, Valentina
N1 - Publisher Copyright:
© The Author(s) 2021. Published by Oxford University Press. All rights reserved.
PY - 2022/12/1
Y1 - 2022/12/1
N2 - In 1986, William Thurston introduced the celebrated (asymmetric) Lipschitz distance on the Teichmüller space of closed or punctured surfaces. We extend his theory to the Teichmüller space of surfaces with boundary endowed with the arc distance. We construct a large family of geodesics for the Teichmüller space of a surface with boundary, generalizing Thurston’s stretch lines. We prove that the Teichmüller space of a surface with boundary is a geodesic and Finsler metric space with respect to the arc distance. As a corollary, we find a new class of geodesics in the Teichmüller space of a closed surface that are not stretch lines in the sense of Thurston.
AB - In 1986, William Thurston introduced the celebrated (asymmetric) Lipschitz distance on the Teichmüller space of closed or punctured surfaces. We extend his theory to the Teichmüller space of surfaces with boundary endowed with the arc distance. We construct a large family of geodesics for the Teichmüller space of a surface with boundary, generalizing Thurston’s stretch lines. We prove that the Teichmüller space of a surface with boundary is a geodesic and Finsler metric space with respect to the arc distance. As a corollary, we find a new class of geodesics in the Teichmüller space of a closed surface that are not stretch lines in the sense of Thurston.
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U2 - 10.1093/imrn/rnab222
DO - 10.1093/imrn/rnab222
M3 - Article
AN - SCOPUS:85146652278
SN - 1073-7928
VL - 2022
SP - 18919
EP - 18991
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 23
ER -