Large scale geometry of certain solvable groups

Geometric and Functional Analysis

Volumn 19, Issue 6, 2010, Pages 1650-1687

  Dymarz, Tullia ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

Analysis on boundaries of negatively curved manifolds; Quasi isometric rigidity; Solvable Lie groups

Indexed keywords

EID: 77952958148     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-010-0046-y     Document Type: Article

References (21)

1. L. Auslander, An exposition of the structure of solvmanifolds, Bull. Amer. Math. Soc. (1973), 227-285.
2. Bridson M. R., Haefliger A.: Metric Spaces of Non-Positive Curvature. Springer-Verlag, Berlin (1999).
3. Chow R.: Groups coarse quasi-isometric to complex hyperbolic space. Trans. Amer. Math. Soc. 348, 1757-1769 (1996).
4. Y. Cornulier, Dimension of asymptotic cones of Lie groups, J. of Topology, to appear.
5. A. Eskin, D. Fisher, K. Whyte, Quasi-isometries and rigidity of solvable groups, Pur. Appl. Math. Q., to appear.
6. A. Eskin, D. Fisher, K. Whyte, Coarse differentiation of quasi-isometries I: Rigidity for Sol and Lamplighter groups, to appear.
7. A. Eskin, D. Fisher, K. Whyte, Coarse differentiation of quasi-isometries II: Rigidity for Sol and Lamplighter groups, to appear.
8. Farb B., Mosher L.: Quasi-isometric rigidity for the solvable Baumslag-Solitar groups II. Invent. Math. 137, 613-649 (1999).
9. Farb B., Mosher L.: On the asymptotic geometry of abelian-by-cyclic groups. Acta Math. 184, 145-202 (2000).
10. B. Farb, L. Mosher, Problems on the geometry of finitely generated solvable groups, Crystallographic Groups and Their Generalizations (Kortrijk, 1999), Contemp. Math. 262, Amer. Math. Soc., Providence, RI (2000), 121-134.
11. Furman A.: Mostow-Margulis rigidity with locally compact targets. Geom. Funct. Anal. 11, 30-59 (2001).
12. Gersten S. M.: Quasi-isometry invariance of cohomological dimension. Comptes Rendues Acad. Sci. Paris Serie 1 Math. 316, 411-416 (1993).
13. F. P. Greenleaf, Invariant Means on Topological Groups, van Nostrand, 1969.
14. Guivarc'h Y.: Sur la loi des grands nombres et le rayon spectral dune marche aléatoire. Ast., Soc. Math. France 74, 47-98 (1980).
15. Mostow G.: Representative functions on discrete groups and solvable arithmetic subgroups. Amer. J. Math. 92, 1-32 (1970).
16. Osin D.: Exponential radicals of solvable Lie groups. J. Algebra 248, 790-805 (2002).
17. I. Peng, The quasi-isometry group of a subclass of solvable Lie groups I, preprint.
18. I. Peng, The quasi-isometry group of a subclass of solvable Lie groups II, preprint.
19. D. Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N. Y., 1978), Ann. of Math. Stud., Princeton Univ. Press, Princeton, NJ, 97 (1981), 465-496.
20. Tukia P.: On quasiconformal groups. Journal d'Analyse Mathematique 46, 318-346 (1986).
21. Tyson J.: Metric and geometric quasiconformality in Ahlfors regular Loewner spaces Conform. Geom. Dyn. 5, 21-73 (2001).