On Isoperimetric Profiles of Finitely Generated Groups

Geometriae Dedicata

Volumn 100, Issue 1, 2003, Pages 157-171

  Erschler, Anna ^a,b  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

Author keywords

Amenable group; F lner sets; Isoperimetric profile; Wreath product

Indexed keywords

EID: 0345865023     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025849602376     Document Type: Article

References (20)

1. Coulhon, Th. and Saloff-Coste, L.: Isopérimétrie pour les groupes et variétés, Rev. Math. Iberoamericana 9 (1993), 293-314.
2. Dyubina, A.: An example of growth rate for random walk on group, Russian Math. Surveys 54 (5) (1999), 1023-1024.
3. Dyubina, A.: Characteristics of random walks on wreath product of groups, Zapiski Nauchn. Sem. POMI 256 (1999), 31-37.
4. Dyubina, A.: Instability of the virtual solvability and the property of being virtually torsion-free for quasi-isometric groups, Internat. Math. Res. Notices 21 (2000), 1097-1101.
5. Erschler (Dyubina), A.: Drift and entropy growth for random walks on groups, Russian Math. Surveys 56 (3) (2001), 179-180.
6. Følner, E.: On groups with full Banach mean value, Math. Scand. 3 (1955), 243-244.
7. Grigorchuk, R. I. and Zuk, A.: The lamplighter group generated by 2-state automaton, and its spectrum, Geom. Dedicata. 87(1) (2001), 209-244.
8. Gromov, M.: Metric Structures for Riemannian and Non-Riemannian Spaces, Progr. in Math. 152, Birkhäuser, Boston, 1999.
9. Gromov, M.: Geometric Group Theory. Volume 2: Asymptotic Invariants of Infinite Groups, London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press, 1993.
10. Kaimanovich, V.: The spectral measure of transition operator and harmonic functions connected with random walks on discrete groups, Zap. Nauchn. Sem. LOMI 97 (1980), 102-109.
11. Kaimanovich, V. A. and Vershik, A. M.: Random walks on discrete groups: Boundary and entropy, Ann. Probab. 11 (1983), 457-490.
12. Pansu, P.: Une inégalité isopérimétrique sur le groupe de Heisenberg, C.R. Acad. Sci. Paris, Sér. I. 295 (1982), 127-130.
13. Pittet, Ch.: The isoperimetric profile of homogeneous Riemannian manifolds, J. Differential Geom. 54 (2000), 255-302.
14. Pittet, Ch. and Saloff-Coste, L.: Amenable groups, isoperimetric profiles and random walks, In: J. Cossey et al. (eds.), Geometric Group Theory Down Under (Canberra, Australia, July 14-19, 1996), de Gruyter, Berlin, 1999, pp. 293-316.
15. Varopoulos, N. Th., Saloff-Coste, L. and Coulhon, T.: Analysis on Lie Groups. Cambridge Tracts in Math., Cambridge Univ. Press, 1992.
16. Varopoulos, N. Th.: Random walks on soluble groups, Bull. Sci. Math. Ser. 2 107 (1983), 337-344.
17. Varopoulos, N. Th.: Chaines de Markov et inégalités isopérimétriques, C.R. Acad. Sci., Paris, Ser. I 298 (1984), 465-468.
18. Vershik, A. M.: Countable groups that are close to finite ones, Appendix in F. P. Greenleaf, Invariant Means on Topological Groups and their Applications, Moscow, Mir, 1973 (in Russian), a revised English translation Amenability and approximation of infinite groups, Selecta Math. 2 (4) (1982), 311-330.
19. Vershik, A. M.: Countable groups that are close to finite ones, Appendix in F. P. Greenleaf, Invariant Means on Topological Groups and their Applications, Moscow, Mir, 1973 (in Russian), a revised English translation Amenability and approximation of infinite groups, Selecta Math. 2 (4) (1982), 311-330.
20. Zuk, A.: On an isoperimetric inequality for infinite finitely generated groups, Topology 39 (5) (2000), 947-956.