Geometry & Topology

Teichmüller geodesics that do not have a limit in $\mathcal{PMF}$

Anna Lenzhen

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Abstract

We construct a Teichmüller geodesic which does not have a limit on the Thurston boundary of the Teichmüller space. We also show that for this construction the limit set is contained in a one-dimensional simplex in P.

Article information

Source
Geom. Topol., Volume 12, Number 1 (2008), 177-197.

Dates
Received: 23 November 2006
Revised: 10 August 2007
Accepted: 25 October 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800017

Digital Object Identifier
doi:10.2140/gt.2008.12.177

Mathematical Reviews number (MathSciNet)
MR2377248

Zentralblatt MATH identifier
1189.30086

Subjects
Primary: 30F60: Teichmüller theory [See also 32G15] 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 32F45: Invariant metrics and pseudodistances 57M50: Geometric structures on low-dimensional manifolds

Keywords
Teichmüller space Thurston's boundary geodesic limit set

Citation

Lenzhen, Anna. Teichmüller geodesics that do not have a limit in $\mathcal{PMF}$. Geom. Topol. 12 (2008), no. 1, 177--197. doi:10.2140/gt.2008.12.177. https://projecteuclid.org/euclid.gt/1513800017


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References

  • L V Ahlfors, Lectures on quasiconformal mappings, second edition, University Lecture Series 38, American Mathematical Society, Providence, RI (2006) With supplemental chapters by C. J. Earle, I. Kra, M. Shishikura and J. H. Hubbard
  • P Buser, Geometry and spectra of compact Riemann surfaces, Progress in Mathematics 106, Birkhäuser, Boston (1992)
  • A Fathi, F Laudenbach, V Poenaru, Travaux de Thurston sur les surfaces, Astérisque 66, Société Mathématique de France, Paris (1979) Séminaire Orsay, with an English summary
  • Y Imayoshi, M Taniguchi, An introduction to Teichmüller spaces, Springer, Tokyo (1992) Translated and revised from the Japanese by the authors
  • A Y Khinchin, Continued fractions, russian edition, Dover Publications, Mineola, NY (1997) With a preface by B. V. Gnedenko, Reprint of the 1964 translation
  • G Levitt, Foliations and laminations on hyperbolic surfaces, Topology 22 (1983) 119–135
  • B Maskit, Comparison of hyperbolic and extremal lengths, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985) 381–386
  • H Masur, Two boundaries of Teichmüller space, Duke Math. J. 49 (1982) 183–190
  • H Masur, S Tabachnikov, Rational billiards and flat structures, from: “Handbook of dynamical systems, Vol. 1A”, (B Hasselblatt, A Katok, editors), North-Holland, Amsterdam (2002) 1015–1089
  • Y N Minsky, Teichmüller geodesics and ends of hyperbolic $3$-manifolds, Topology 32 (1993) 625–647
  • K Strebel, Quadratic differentials, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 5, Springer, Berlin (1984)