Generalized Harmonic Maps and Representations of Discrete Groups

Communications in Analysis and Geometry

Volumn 8, Issue 3, 2000, Pages 545-563

  Wang, Mu Tao ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038563973     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/CAG.2000.v8.n3.a5     Document Type: Article

References (25)

1. 2-cohomology and property (T) for automorphism groups of polyhedral cell complexes, GAFA, 7 (1997), 615-645.
2. K. Brown, Buildings, Springer-Verlag, New York 1989.
3. F. Bruhat J. and Tits, Groupes réductifs sur un corps local. I. Données radicielles valuées, Inst. Hautes Études Sci. Publ. Math. 41 (1972), 5-251.
4. E. Calabi and E. Vesentini, On compact, locally symmetric Kahler manifolds, Ann. Math. 71 (1960), 472-507.
5. K. Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. Math. 135 (1992), 165-182.
6. H. Garland, p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann. Math. 97 (1973), 375-423.
7. M. Gromov and R. Schoen, Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, Publ. I.H.E.S. 76 (1992), 165-246.
8. C. Hodgson and S. Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998), no. 1, 1-59.
9. J. Jost, Generalized harmonic maps between metric spaces, in Geometric Analysis and the Calculus of Variations for Stefan Hildebrandt, edited by J. Jost, International Press, 1996.
10. J. Jost and S-T. Yau, Harmonic maps and superrigidity, Proceedings of Symposia in Pure Mathemaitcs, 54 (1993) Part I, AMS, 245-280.
11. N. Korevaar and R. Schoen, Sobolev spaces and harmonic maps for metric space target, Comm. Anal. Geom, 1 (1993), 561-659.
12. G.A. Margulis, Discrete subgroups of semisimple Lie groups, Springer-Verlag, 1991.
13. G.A. Margulis, Superrigidity for commensurability subgroups and generalized harmonic maps, preprint.
14. Y. Matsushima, On the first Betti number of compact quotient spaces of higher dimensional symmetric spaces, Ann. of Math. 75 (1962), 312-330.
15. N. Mok, Y.T. Siu, S.K. and Yeung, Geometric superrigidity , Invent. Math., 113 (1993), 57-83.
16. I. Nikolaev, The tangent cone of an Aleksandrov space of curvature ≤ K, Manuscripta Mathematica, 86 (1995), 137-147.
17. P. Pansu, Formule de Matsushima, de Garland, et propriete (T) pour des groupes agissant sur des espaces symetriques ou des immeubles, preprint (Orsay 1996).
18. Y.G. Reshetnyak, Nonexpanding maps in a space of curvature no greater than K, Siberian Math. Journ. 9 (1968), 918-927.
19. M. Ronan, Lectures on Buildings, Academic Press, San Diego 1989.
20. Y.T. Siu, The complex analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. Math. 112 (1980), 73-111.
21. M-T. Wang, A fixed point theorem of discrete group actions on Riemannian manifolds, J. Differential Geom 50 (1998), no.2, 247-267.
22. M-T. Wang, Fixed point theorems and property (T), preprint, 1998.
23. A. Weil, Discrete subgroups of Lie groups II, Ann. Math. 75 (1962), 578-602.
24. R. Zimmer, Ergodic theory and semisimple groups, Birkhaüser, 1984.
25. A. Zuk, La propriete (T) de Kazhdan pour les groupes agissant sur les polydres, C. R. Acad. Sci. Paris 323, Serie I (1996), 453-458.