### Impacto

Díaz Sánchez, Raquel and Inkang, Kim
(2012)
*Asymptotic behabior of grafting rays.*
Geometriae dedicata, 158
(1).
pp. 267-281.
ISSN 1572-9168

PDF
Restringido a Repository staff only hasta 31 December 2020. 285kB |

Official URL: http://www.springerlink.com/content/k305h1856v7g3128/fulltext.pdf

## Abstract

In this paper we study the convergence behavior of grafting rays to the Thurston boundary of Teichmuller space. When the grafting is done along a weighted system of simple closed curves or along a maximal uniquely ergodic lamination this behavior is the same as for Teichmuller geodesics and lines of minima. We also show that the ray grafted along a weighted system of simple closed curves is at bounded distance from Teichmuller geodesic.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Projective structure; Hyperbolic structure; Grafting; Teichmüller space |

Subjects: | Sciences > Mathematics > Geometry |

ID Code: | 15717 |

References: | Abikoff, W.: The Real Analytic Theory of Teichmüller Space. Springer, Berlin (1980) Choi, Y., Rafi, K.: Comparison between Teichmüller and Lipschitz metrics. J. Lond. Math. Soc. 76, 739–756 (2007) Choi, Y., Rafi, K., Series, C.: Lines of minima and Teichmüller geodesics. GAFA 18(3), 698–754 (2008) Díaz, R., Series, C.: Limit points of lines of minima in Thurston’s boundary of Teichmüller space. Alg. Geom. Top. 3, 207–234 (2003) Dumas, D.: Grafting, pruning, and the antipodalmap on measured laminations. J. Diff. Geom. 74, 93–118 (2006) Dumas, D., Wolf, M.: Projective structures, grafting, and measured laminations. Geom. Top. 12(1),351–386 (2008) Gardiner, F.: Teichmüller Theory and Quadratic Differentials. Wiley, London (1987) Hensel, S.: Iterated grafting and holonomy lifts of Teichmüller space. Geometr. Ded. (2011) Hubbard, J., Masur, H.: Quadratic differentials and foliations. Acta Math. 142, 221–274 (1979) Kamishima, Y., Tan, S.: Deformation spaces on geometric structures. In: Aspects of low-dimensional manifolds, vol. 20 of Advanced Studies in Pure Mathematics, Kinokuniya, Tokyo, pp 263–299 (1992) Kerckhoff, S.: The asymptotic geometry of Teichmüller space. Topology 19, 23–41 (1980) Kerckhoff, S.: Lines of minima in Teichmüller space. Duke Math. J. 65, 187–213 (1992) Lenzhen, A.: Teichmüller geodesics which do not converge. Geom. Top. 12, 177–197 (2008) Masur, H.: On a class of geodesics in Teichmüller space. Ann. Math. 102(2), 205–221 (1975) Masur, H.: Two boundaries of Teichmüller space. Duke Math. J. 49, 183–190 (1982) McMullen, C.T.: Complex earthquakes and Teichmüller theory. J. Am. Math. Soc. 11(2), 283–320 (1998) Minsky, Y.N.: Extremal length estimates and product regions in Teichmüller space. Duke Math. J. 83(2), 249–286 (1996) Scannell, K., Wolf, M.: The grafting map of Teichmüller space. J. AMS 15(4), 893–927 (2002) Tanigawa, H.: Grafting, harmonic maps and projective structures on surfaces. J. Diff. Geom. 47, 399–419 (1997) Wolpert, S.: The length spectra as moduli for compact Riemann surfaces. Ann. Math. 109(2), 323–351 (1979) |

Deposited On: | 21 Jun 2012 11:10 |

Last Modified: | 06 Feb 2014 10:30 |

Repository Staff Only: item control page