Harmonic maps to Teichmüller space

Mathematical Research Letters

Volumn 7, Issue 1, 2000, Pages 133-146

  Daskalopoulos, Georgios ^a   Katzarkov, Ludmil ^b   Wentworth, Richard ^b  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034349833     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.2000.v7.n1.a12     Document Type: Article

References (38)

1. [ABKP] J. Amorós, F. Bogomolov, L. Katzarkov, and T. Pantev, Symplectic Lefschetz fibrations with arbitrary fundamental group, preprint, GT/9810042.
2. [Chu] T. Chu, The Weil-Petersson metric in moduli space, Chinese J. Math. 4 (1976), 29-51.
3. [C1] K. Corlette, Flat G-bundles with canonical metrics, J. Diff. Geom. 28 (1988), 361-382.
4. [C2] _, unpublished.
5. [D1] S. Donaldson, Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc. (3) 55 (1987), 127-131.
6. [D2] _, Lefschetz fibrations in symplectic geometry, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Doc. Math., 1998, Extra Volume II, 309-314.
7. [FLP] A. Fathi, F. Laudenbach, and V. Poénaru, Travaux de Thurston sur les surfaces, Astérisque, 66-67, Soc. Math. France, Paris, 1979.
8. [GoSt] R. Gompf and A. Stipsicz, An introduction to 4-manifolds and Kirby calculus, Graduate Studies in Mathematics, 20, American Mathematical Society, Providence, RI, 1999.
9. [GS] M. Gromov and R. Schoen, Harmonic maps into singular spaces and p-adic super-rigidity for lattices in groups of rank one, Inst. Hautes Études Sci. Publ. Math., 76, (1992), 165-246.
10. [J1] J. Jost, Equilibrium maps between metric spaces, Calc. Var. Partial Differential Equations 2 (1994), 173-204.
11. [J2] _, Harmonic maps between surfaces, Lecture Notes in Mathematics, 1062, Springer-Verlag, Berlin-New York, 1984.
12. [J3] _, Minimal surfaces and Teichmüller theory, in Tsing Hua lectures on geometry and analysis, Hsinchu, Taiwan, 1990-92, International Press, Cambridge, MA, 1995, pp. 149-211.
13. [JY1] J. Jost and S.-T. Yau, Harmonic maps and group representations, in Differential geometry (H.B. Lawson and K. Tenenblat, eds.), Pitman Monographs Surveys Pure Appl. Math., 52, Longman Sci. Tech., Harlow, 1991, pp. 241-260.
14. [JY2] _, On the rigidity of certain discrete groups and algebraic varieties, Math. Ann. 278 (1987), 481-496.
15. [JY3] _, Harmonic mappings and algebraic varieties over function fields, Amer. J. Math. 115 (1993), 1197-1227.
16. [K] S. Kerckhoff, The Nielsen realization problem, Ann. of Math. 117 (1983), 235-265.
17. [KM] V. Kaimanovich and H. Masur, The Poisson boundary of the mapping class group, Invent. Math. 125 (1996), 221-264.
18. [KPS] L. Katzarkov, T. Pantev, and C. Simpson, Nonabelian open orbit theorems, in preparation.
19. [KS] N. Korevaar and R. Schoen, Sobolev spaces and harmonic maps for metric space targets, Comm. Anal. Geom. 1 (1993), 561-659.
20. [La] F. Labourie, Existence d'applications harmoniques tordues à valeurs dans les variétés à courbure négative, Proc. Amer. Math. Soc. 111 (1991), 877-882.
21. [Le] L. Lemaire, Applications harmoniques de surfaces riemanniennes, J. Differential Geom. 13 (1978), 51-78.
22. [L] E. Looijenga, Smooth Deligne-Mumford compactifications by means of Prym level structures, J. Algebraic Geom. 3 (1994), 283-293.
23. [M] H. Masur, On a class of geodesics in Teichmüller space, Ann. of Math. 102 (1975), 205-221.
24. [MM] Y. Matsumoto and J. Montesinos-Amilibia, Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces, Bull. Amer. Math. Soc. 30 (1994), 70-75.
25. [McM] C. McMullen, The moduli space of Riemann surfaces is Kähler hyperbolic, preprint, 1999, available at www.math.harvard.edu7ctm
26. [MP] J. McCarthy and A. Papadopoulos, Dynamics on Thurston's sphere of projective measured foliations, Comment. Math. Helv. 64 (1989), 133-166.
27. [Re] M. Rees, An alternative approach to the ergodic theory of measured foliations on surfaces, Ergodic Theory Dynamical Systems 1 (1981), 461-488.
28. [R] H. Royden, unpublished.
29. [SU] J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. of Math. 113 (1981), 1-24.
30. [SY] R. Schoen and S.-T. Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. Math. 110 (1981), 127-142.
31. [Sm] I. Smith, Symplectic geometry of Lefschetz fibrations, Oxford Thesis, 1999.
32. [T] A. Tromba, On a natural algebraic affine connection on the space of almost complex structures and the curvature of Teichmüller space with respect to the Weil-Petersson metric, Manuscripta Math. 56 (1986), 475-497.
33. [Wo] M. Wolf, The Teichmüller theory of harmonic maps, J. Differential Geom. 29 (1989), 449-479.
34. [W1] S. Wolpert, Chern forms and the Riemann tensor for the moduli space of curves, Invent. Math. 85 (1986), 119-145.
35. [W2] _, Geodesic length functions and the Nielsen problem, J. Differential Geom. 25 (1987), 275-296.
36. [W3] _, Noncompleteness of the Weil-Petersson metric for Teichmüller space, Pacific J. Math. 61 (1975), 573-577.
37. [W4] _, The length spectra as moduli for compact Riemann surfaces, Ann. of Math. 109 (1979), 323-351.
38. [W5] _, On the Weil-Petersson geometry of the moduli space of curves, Amer. J. Math. 107 (1985), 969-997.