Extremal length estimates and product regions in teichmüller space

Duke Mathematical Journal

Volumn 83, Issue 2, 1996, Pages 249-286

  Minsky, Yair N ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009197644     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-96-08310-6     Document Type: Article

References (30)

1. W. ABIKOFF, The Real Analytic Theory of Teichmüller Space, Lecture Notes in Math. 820, Springer-Verlag, New York, 1980.
2. L. AHLFORS, Conformal Invariants: Topics in Geometric Function Theory, McGraw-Hill, New York, 1973.
3. A. F. BEARDON, The Geometry of Discrete Groups, Grad. Texts in Math. 91, Springer-Verlag, New York, 1983.
4. L. BERS, "Spaces of degenerating Riemann surfaces" in Discontinuous Groups and Riemann Surfaces, Ann. of Math. Stud. 79, Princeton Univ. Press, Princeton, 1974, 43-55.
5. J. CANNON, "The theory of negatively curved spaces and groups" in Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces (Trieste, 1989), Oxford Univ. Press, New York, 1991, 315-369.
6. M. COORNAERT, T. DELZANT, AND A. PAPADOPOULOS, Géométrie et Theorie des Groupes, Lecture Notes in Math. 1441, Springer-Verlag, Berlin, 1990.
7. C. J. EARLE AND A. MARDEN, Geometric complex coordinates for Teichmüller space, manuscript.
8. A. FATHI, F. LAUDENBACH, AND V. POENARU, EDS., Travaux de Thurston sur les surfaces, Astérisque 66-67 (1979).
9. J. D. FAY, Theta Functions on Riemann Surfaces, Lecture Notes in Math. 352, Springer-Verlag, New York, 1973.
10. W. FENCHEL AND J. NIELSEN, Discontinuous groups of non-Euclidean motions, unpublished manuscript.
11. R. FRICKE AND F. KLEIN, Vorlesungen über die Theorie der automorphen Funktionen, Teubner, Leipzig, 1897, 1912.
12. M. GROMOV, "Hyperbolic groups" in Essays in Group Theory, ed. by S. M. Gersten, Math. Sci. Res. Inst. Publ. 8, Springer-Verlag, New York, 1987.
13. D. HEJHAL, Regular b-groups, degenerating Riemann surfaces, and spectral theory, Mem. Amer. Math. Soc. 88 (1990), no. 437.
14. L. KEEN, "Collars on Riemann surfaces" in Discontinuous Groups and Riemann Surfaces, Ann. of Math. Stud. 79, Princeton Univ. Press, Princeton, 1974, 263-268.
15. S. KERCKHOFF, The asymptotic geometry of Teichmüller space, Topology 19 (1980), 23-41.
16. I. KRA, Horocyclic coordinates for Riemann surfaces and moduli spaces, I: Teichmüller and Riemann spaces of Kleinian groups, J. Amer. Math. Soc. 3 (1990), 499-578.
17. B. MASKIT, Decomposition of certain Kleinian groups, Acta Math. 130 (1973), 243-263.
18. _, Moduli of marked Riemann surfaces. Bull. Amer. Math. Soc. 80 (1974), 773-777.
19. _, Comparison of hyperbolic and extremal lengths, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 381-386.
20. H. A. MASUR, On a class of geodesics in Teichmul̈ler space, Ann. of Math. (2) 102 (1975), 205-221.
21. _, Extension of the Weil-Petersson metric to the boundary of Teichmüller space, Duke Math. J. 43 (1976), 623-635.
22. _, Transitivity properties of the horocyclic and geodesic flows on moduli space, J. Anal. Math. 39 (1981), 1-10.
23. _, Two boundaries of Teichmüller space, Duke Math. J. 49 (1982), 183-190.
24. H. A. MASUR AND M. WOLF, Teichmüller space is not Gromov hyperbolic, Math. Sci. Res. Inst. preprint no. 011-94, 1994.
25. Y. MINSKY, Harmonic maps, length, and energy in Teichmüller space, J. Differential Geom. 35 (1992), 151-217.
26. _, Teichmüller geodesics and ends of hyperbolic 3-manifolds, Topology 32 (1993), 625-647.
27. M. WOLF AND S. A. WOLPERT, Real analytic structures on the moduli space of curves, Amer. J. Math. 114 (1992), 1079-1102.
28. S. A. WOLPERT, On the Weil-Petersson geometry of the moduli space of curves, Amer. J. Math. 107 (1985), 969-997.
29. _, Cut-and-paste deformations of Riemann surfaces, Ann. Acad. Sci. Fenn. Ser A I Math. 13 (1988), 401-413.
30. _, The hyperbolic metric and the geometry of the universal curve, J. Differential Geom. 31 (1990), 417-472.