Teichmüller geodesics that do not have a limit in \(\mathcal PMF\). (English) Zbl 1189.30086
Summary: 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 \(\mathcal{PMF}\).
MSC:
| 30F60 | Teichmüller theory for Riemann surfaces |
| 32G15 | Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) |
| 32F45 | Invariant metrics and pseudodistances in several complex variables |
| 57M50 | General geometric structures on low-dimensional manifolds |
References:
| [1] | L V Ahlfors, Lectures on quasiconformal mappings, University Lecture Series 38, American Mathematical Society (2006) · Zbl 0138.06002 |
| [2] | P Buser, Geometry and spectra of compact Riemann surfaces, Progress in Mathematics 106, Birkhäuser (1992) · Zbl 0770.53001 |
| [3] | A Fathi, F Laudenbach, V Poenaru, Travaux de Thurston sur les surfaces, Astérisque 66, Société Mathématique de France (1979) 284 |
| [4] | Y Imayoshi, M Taniguchi, An introduction to Teichmüller spaces, Springer (1992) · Zbl 0754.30001 |
| [5] | A Y Khinchin, Continued fractions, Dover Publications (1997) · Zbl 0117.28601 |
| [6] | G Levitt, Foliations and laminations on hyperbolic surfaces, Topology 22 (1983) 119 · Zbl 0522.57027 · doi:10.1016/0040-9383(83)90023-X |
| [7] | B Maskit, Comparison of hyperbolic and extremal lengths, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985) 381 · Zbl 0587.30043 |
| [8] | H Masur, Two boundaries of Teichmüller space, Duke Math. J. 49 (1982) 183 · Zbl 0508.30039 · doi:10.1215/S0012-7094-82-04912-2 |
| [9] | H Masur, S Tabachnikov, Rational billiards and flat structures (editors B Hasselblatt, A Katok), North-Holland (2002) 1015 · Zbl 1057.37034 |
| [10] | Y N Minsky, Teichmüller geodesics and ends of hyperbolic \(3\)-manifolds, Topology 32 (1993) 625 · Zbl 0793.58010 · doi:10.1016/0040-9383(93)90013-L |
| [11] | K Strebel, Quadratic differentials, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 5, Springer (1984) · Zbl 0547.30001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
