Superrigidity, generalized harmonic maps and uniformly convex spaces

Geometric and Functional Analysis

Volumn 17, Issue 5, 2008, Pages 1524-1550

  Gelander, Tsachik ^a   Karlsson, Anders ^b   Margulis, Gregory A ^c  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^c YALE UNIVERSITY   (United States)

Author keywords

Metric geometry; Superrigidity

Indexed keywords

EID: 39549114821     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-007-0639-2     Document Type: Article

References (20)

1. U. BADER, A. FURMAN, T. GELANDER, N. MONOD, Property (T) and fixed rigidity for actions on Banach spaces, Acta Mathematica 198 (2007), 57-105.
2. Y. BENYAMINI, J. LINDENSTRAUSS, Geometric Nonlinear Functional Analysis, vol. 1, American Mathematical Society Colloquium Publications 48, American Mathematical Society, Providence, RI, 2000.
3. M. BRIDSON, A. HAEFLIGER, Metric Spaces of Non-Positive Curvature, Grundl. der Math. Wiss. 319, Springer Verlag, 1999.
4. H. BUSEMANN, Spaces with non-positive curvature, Acta Mathematica 80 (1948), 259-310.
5. K. CORLETTE, Archimedian superrigidity and hyperbolic geometry, Ann. Math. 135 (1992), 165-182.
6. T. FOERTSCH, Ball versus distance convexity of metric spaces, Beitrge Algebra Geom. 45 (2004), 481-500.
7. M. GROMOV, R. SCHOEN, Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one, Inst. Hautes Etudes Sei. Publ. Math. 76 (1992), 165-246.
8. P. DE LA HARPE, Classical Banach-Lie Algebras and Banach-Lie Groups of Operators in Hilbert Space, Springer Lecture Notes in Mathematics 285 (1972).
9. J. JOST, Nonpositive Curvature: Geometric and Analytic Aspects, Lectures in Math. ETH Zürich, Birkhuser Verlag, 1997.
10. G.A. MARGULIS, Discrete subgroups of motions of manifolds of nonpositive curvature, Amer. Math. Soc. Translations 109 (1977), 33-45.
11. G.A. MARGULIS, Discrete Subgroups of Semisimple Lie Groups, Ergeb. Math., Springer-Verlag, 1991.
12. G.A. MARGULIS, Arithmeticity of the irreducible lattices in the semisimple groups of rank grater than 1, Invent. Math. 76 (1984), 93-120.
13. G.A. MARGULIS, Superrigidity for commensurability subgroups and generalized harmonic maps, unpublished manuscript.
14. N. MONOD, Superrigidity for irreducible lattices and geometric splitting, J. Amer. Math. Soc. 19:4 (2006), 781-814.
15. K.H. NEEB, A Cartan-Hadamard theorem for Banach-Finsler manifolds, (English summary) Proceedings of the Conference on Geometric and Combinatorial Group Theory, Part II (Haifa, 2000), Geom. Dedicata 95 (2002), 115-156.
16. P. PANSU, Geometric superrigidity, preprint 2006.
17. A. PAPADOPOULOS, Metric spaces, Convexity and Nonpositive Curvature IRMA Lectures in Mathematics and Theoretical Physics 6, European Mathematical Society (EMS), Zürich, 2005.
18. B. REMY, Integrability of induction cocycles for Kac-Moody groups, Math. Ann. 333 (2005), 29-43.
19. Y. SHALOM, Rigidity of commensurators and irreducible lattices, Invent. Math. 141 (2000), 196-220.
20. H. UPMEIER, Some applications of infinite-dimensional holomorphy to mathematical physics, Aspects of Mathematics and its Applications, North-Holland Math. Library, 34, North-Holland, Amsterdam (1986), 817-832.