Combinatorial harmonic maps and discrete-group actions on Hadamard spaces

Geometriae Dedicata

Volumn 114, Issue 1, 2005, Pages 147-188

  Izeki, Hiroyasu ^a   Nayatani, Shin ^b  

^a TOHOKU UNIVERSITY   (Japan)

^b NAGOYA UNIVERSITY   (Japan)

Author keywords

Building; Discrete group; Hadamard space; Harmonic map; Simplicial complex; Superrigidity

Indexed keywords

EID: 24644480155     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10711-004-1843-y     Document Type: Article

References (34)

1. 2-cohomology and property (T) for automorphism groups of polyhedral cell complexes, Geom. Funct. Anal. 7 (1997), 615-645.
2. Bridson, M. R. and Haefliger, A.: Metric Spaces of Non-positive Curvature, Springer-Verlag, Berlin, 1999.
3. Brown, K. S.: Buildings, Springer-Verlag, New York, 1988.
4. Corlette, K.: Flat G-bundles with canonical metrics, J. Differential Geom. 28 (1988), 361-382.
5. Corlette, K.: Archimedian superrigidity and hyperbolic geometry, Ann. Math. 135 (1992), 165-182.
6. Donaldson, S. K.: Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc. 55 (1987), 127-131.
7. Eells, J. and Sampson, J. H.: Harmonic maps of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160.
8. Feit, W. and Higman, G.: The nonexistence of certain generalized polygons, J. Algebra 1 (1964), 114-131.
9. Garland, H.: p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann. Math. 97 (1973), 375-423.
10. Gromov, M.: Asymptotic invariants of infinite groups, Geom. Group Theory, 2 (Sussex, 1991), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press, Cambridge, 1993, 1-295.
11. Gromov, M.: Random walk in random groups, Geom. Funct. Anal. 13 (2003), 73-148.
12. Gromov, M. and Schoen, R.: Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, Publ. Math. IHES 76 (1992), 165-246.
13. de la Harpe, P. and Valette, A.: La propriété (T) de Kazhdan pour les groupes localement compactes, Astérisque 175 (1989).
14. Izeki, H. and Nayatani, S.: Combinatorial harmonic maps and superrigidity (Japanese), In: Hyperbolic Spaces and Discrete Groups II (Kyoto, 2001), RIMS Kokyuroku 1270 (2002), 182-194.
15. Izeki, H. and Nayatani, S.: Combinatorial harmonic maps and superrigidity - the case of singular target (Japanese), Perspectives of Hyperbolic Spaces (Kyoto, 2002), RIMS Kokyuroku 1329 (2003), 1-7.
16. Jost, J.: Equilibrium maps between metric spaces, Calc. Var. 1 (1997), 173-204.
17. Jost, J.: Convex functionals and generalized harmonic maps into spaces of nonpositive curvature, Comment. Math. Helv. 70 (1995), 659-673.
18. Jost, J.: Nonpositive Curvature: Geometric and Analytic Aspects, Lect. Math. ETH Zürich, Birkhäuser, Basel, 1997.
19. Jost, J.: Nonlinear Dirichlet forms, In New Directions in Dirichlet Forms, Stud. Adv. Math. Amer. Math. Soc., Providence, 1998, pp. 1-48.
20. Jost, J. and Yau, S.-T.: Harmonic maps and group representations. In: B. Lawson and K. Tenenblat (eds), Differential Geometry and Minimal Submanifolds, Longman Scientific, Harlow, 1991, pp. 241-259.
21. Jost, J. and Yau, S.-T.: Harmonic maps and superrigidity, Differential geometry: partial differential equations on manifolds, Proc. Sympos. Pure Math. 54-1 (1993), 245-280.
22. Korevaar, M. and Schoen, R.: Sobolev spaces and harmonic maps for metric space targets, Comm. Anal. Geom. 1 (1993), 561-659.
23. Kotani, M. and Sunada, T.: Standard realizations of crystal lattices via harmonic maps, Trans. Amer. Math. Soc. 353 (2000), 1-20.
24. Labourie, F.: Existence d'applications harmoniques tordues à valeurs dans les variété à coubure négative, Proc. Amer. Math. Soc. 111 (1991), 877-882.
25. Lebeau, É.: Applications harmoniques entre graphes finis et un théorème de superrigidité, Ann. inst. Fourier 46 (1996), 1183-1203.
26. Margulis, G.: Discrete groups of motions of manifolds of nonpositive curvature, Amer. Math. Soc. Trans. 190 (1997), 33-45.
27. Mayer, U. F.: Gradient flows on nonpositively curved metric spaces and harmonic maps, Comm. Anal. Geom. 6 (1998), 199-253.
28. Mok, N., Siu, Y.-T. and Yeung, S.-K.: Geometric superrigidity, Invent. Math. 113 (1993), 57-83.
29. Pansu, P.: Formules de Matsushima, de Garland et propriété (T) pour des groupes agissant sur des espaces symétriques ou des immeubles, Bull. Soc. Math. France 126 (1998), 107-139.
30. Sarnak, P.: Some Applications of Modular Forms, Cambridge Tracts in Math. 99, Cambridge Univ. Press, 1990.
31. Wang, M.-T.: A fixed point theorem of discrete group actions on Riemannian manifolds, J. Differential Geom. 50 (1998), 249-267.
32. Wang, M.-T.: Generalized harmonic maps and representations of discrete groups, Comm. Anal. Geom. 8 (2000), 545-563.
33. Żuk, A.: La propriété (T) de Kazhdan pour les groupes agissant sur les polyédres, C.R. Acad. Sci. Paris 323 (1996), 453-458.
34. Żuk, A.: Property (T) and Kazhdan constants for discrete groups, Geom. Funet. Anal. 13 (2003), 643-670.