Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-28T05:26:46.108Z Has data issue: false hasContentIssue false
  • English
  • Français

The geometry of measured geodesic laminations and measured train tracks

Published online by Cambridge University Press:  19 September 2008

Howard Weiss
Howard Weiss
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Thurston and Kerckhoff have shown that the space of measured geodesic laminations on a hyperbolic Riemann surface serves as a non-linear model of the tangent space to Teichmüller space at the surface. In this paper we show that the natural map between these manifolds has stronger than Hölder continuous regularity.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 3 , September 1989 , pp. 587 - 604
Copyright
Copyright © Cambridge University Press 1989

References

REFERENCES

[BE]Beardon, A.. The Geometry of Discrete Groups Springer Verlag: New York, NY, 1983.CrossRefGoogle Scholar
[BS]Birman, J. & Series, C.. Simple curves have Hausdorff dimension one. Preprint.Google Scholar
[HP]Harer, J. & Penner, R.. Combinatorics of train tracks. To appear.Google Scholar
[K1,]Kerckhoff, S.. The Nielsen realization problem. Ann. Math. 117 (1983), 235–265.CrossRefGoogle Scholar
[K2]Kerckhoff, S.. Earthquakes are analytic. Comm. Math. Helvetia 60 (1985).Google Scholar
[K3]Kerckhoff, S.. Lines of Minima in Teichmüller space. To appear.Google Scholar
[MOO]Moore, R.L.. Concerning upper semi-continuous collections of continua. Trans. Amer. Math. Soc. 11 (1925), 416–428.CrossRefGoogle Scholar
[MOR]Morgan, J.. Columbia University Lecture Notes.Google Scholar
[N]Nicholls, P.. Transitivity properties of fuchsian groups. Canad. J. Math. XXVIII #4 (1976), 805–814.CrossRefGoogle Scholar
[T]Thurston, W.P.. The geometry and topology of 3-manifolds. Princeton University Lecture Notes.Google Scholar
[W,]Wolpert, S.. University of Maryland Lecture Notes.Google Scholar