Lengths of simple loops on surfaces with hyperbolic metrics
| dc.creator | Luo, Feng | |
| dc.creator | Stong, Richard | |
| dc.date | 2002-11-27 | |
| dc.date.accessioned | 2026-07-07T04:53:20Z | |
| dc.date.available | 2026-07-07T04:53:20Z | |
| dc.description | Given a compact orientable surface of negative Euler characteristic, there exists a natural pairing between the Teichmueuller space of the surface and the set of homotopy classes of simple loops and arcs. The length pairing sends a hyperbolic metric and a homotopy class of a simple loop or arc to the length of geodesic in its homotopy class. We study this pairing function using the Fenchel-Nielsen coordinates on Teichmueller space and the Dehn-Thurston coordinates on the space of homotopy classes of curve systems. Our main result establishes Lipschitz type estimates for the length pairing expressed in terms of these coordinates. As a consequence, we reestablish a result of Thurston-Bonahon that the length pairing extends to a continuous map from the product of the Teichmueller space and the space of measured laminations. | |
| dc.description | Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper17.abs.html | |
| dc.identifier | https://arxiv.org/abs/math/0211421 | |
| dc.identifier | http://arxiv.org/abs/math/0211421 | |
| dc.identifier | Geom. Topol. 6(2002) 495-521 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65808 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 30F60, 57M50, 57N16 | |
| dc.title | Lengths of simple loops on surfaces with hyperbolic metrics | |
| dc.type | text |