Quasi-flats and rigidity

in higher rank symmetric spaces

Authors:
Alex Eskin and Benson Farb

Journal:
J. Amer. Math. Soc. **10** (1997), 653-692

MSC (1991):
Primary 22E40, 20F32

MathSciNet review:
1434399

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References | Similar Articles | Additional Information

**[BGS]**Werner Ballmann, Mikhael Gromov, and Viktor Schroeder,*Manifolds of nonpositive curvature*, Progress in Mathematics, vol. 61, Birkhäuser Boston, Inc., Boston, MA, 1985. MR**823981****[E]**A. Eskin,*Quasi-isometric rigidity of higher rank nonuniform lattices*, preprint.**[EF]**A. Eskin and B. Farb,*Quasi-flats in*, to appear in*Proceedings of the Colloquium on Lie Groups and Ergodic Theory, Tata Institute (Jan 1996)*.**[FS]**B. Farb and R. Schwartz,*The large-scale geometry of Hilbert modular groups*, J. Diff. Geom.**44**, No. 3, (1996) pp 435-478.**[KL]**B. Kleiner and B. Leeb,*Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings*, to appear in Publ. IHES.**[He]**Sigurdur Helgason,*Differential geometry, Lie groups, and symmetric spaces*, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR**514561****[Mo]**G. D. Mostow,*Strong rigidity of locally symmetric spaces*, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1973. Annals of Mathematics Studies, No. 78. MR**0385004****[Pa]**Pierre Pansu,*Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un*, Ann. of Math. (2)**129**(1989), no. 1, 1–60 (French, with English summary). MR**979599**, 10.2307/1971484**[Sc]**Henrik Schlichtkrull,*Hyperfunctions and harmonic analysis on symmetric spaces*, Progress in Mathematics, vol. 49, Birkhäuser Boston, Inc., Boston, MA, 1984. MR**757178****[Ti]**Jacques Tits,*Buildings of spherical type and finite BN-pairs*, Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin-New York, 1974. MR**0470099**

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Additional Information

**Alex Eskin**

Email:
eskin@math.uchicago.edu

**Benson Farb**

Email:
farb@math.uchicago.edu

DOI:
http://dx.doi.org/10.1090/S0894-0347-97-00238-5

Keywords:
Lie groups,
discrete subgroups,
geometric group theory

Received by editor(s):
March 8, 1996

Received by editor(s) in revised form:
March 10, 1997

Additional Notes:
Both authors are supported in part by N.S.F. Postdoctoral Fellowships. The work of the second author at MSRI was supported by NSF grant DMS-9022140.

Article copyright:
© Copyright 1997
American Mathematical Society