[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2007.44.5.1051

AMALGAMATED PRODUCTS, CRITICAL EXPONENTS AND UNIFORM GROWTH OF GROUPS: A UNIFIED APPROACH

Besson, Gerard (Institut Fourier and C.N.R.S. Universite de Grenoble I)

Publication Information

Journal of the Korean Mathematical Society / v.44, no.5, 2007 , pp. 1051-1063 More about this Journal

Abstract

The aim of this note is to advertise a method which turns out to be powerful enough to be used successfully in problems which are apparently unrelated. It is based on a modification of a construction that we first introduced in [2].

Keywords

entropy; barycenter; critical exponents; amalgamated products; growth of groups;

Citations & Related Records

Times Cited By Web Of Science : 1 (Related Records In Web of Science)
Times Cited By SCOPUS : 1

Reference
Cited By SCOPUS

1	G. Besson, G. Courtois, and S. Gallot, Uniform growth of groups acting on Cartan-Hadamard spaces, In preparation, 2006
2	Yu. D. Burago and V. A. Zalgaller, Geometric inequalities, Grundlehren der Mathematischen Wissenschaften, 285. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin, 1988
3	G. Carron and E. Pedon, On the differential form spectrum of hyperbolic manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004), no. 4, 705-747
4	W. Balmann, M. Gromov, and V. Schroder, Manifolds of nonpositive curvature, volume 61 of Progress in Maths. Birkhauser, 1985
5	G. Besson, G. Courtois, and S. Gallot, Entropies et rigidites des espaces localement symetriques de courbure strictement negative, Geom. Funct. Anal. 5 (1995), no. 5, 731-799 DOI
6	G. Besson, G. Courtois, and S. Gallot, Rigidity of amalgamated products in negative curvature, Submitted to Journal of Diff. Geom., 2005
7	E. Breuillard and T. Gelander, Cheeger constant and algebraic entropy of linear groups, Int. Math. Res. Not. 2005 (2005), no. 56,3511-3523 DOI
8	A. Eskin, S. Mozes, and H. Oh, On uniform exponential growth for linear groups, Invent. Math. 160 (2005), no. 1, 1-30 DOI
9	F. T. Farrell and P. Ontaneda, Exotic structures and the limitations of certain analytic methods in geometry, Asian J. Math. 8 (2004), no. 4, 639-651 DOI
10	M. Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983), no. 1, 1147
11	Th. Roblin, Ergodicite et equidistribution. en courbure negative, Mem. Soc. Math. Fr. (N.S.) No. 95 (2003), 1-96
12	M. Gromov, Volume and bounded cohomology, Inst. Hautes Etudes Sci. Publ. Math. No. 56 (1982), 5-99
13	A. Lubotzky, Free quotients and the first Betti number of some hyperbolic manifolds, Transform. Groups 1 (1996), no. 1-2, 71-82 DOI
14	J.-F. Quint, Mesures de Patterson-Sullivan en rang superieur, Geom. Funct. Anal. 12 (2002), no. 4, 776-809 DOI
15	J.-P. Serre, Arbres, amalgames, $SL_2$ , Avec un sommaire anglais. Redige avec la collaboration de Hyman Bass. Asterisque, No. 46. Societe Mathematique de France, Paris, 1977
16	Y. Shalom, Rigidity, unitary representations of semisimple groups, and fundamental groups of manifolds with rank one transformation group, Ann. of Math. (2) 152 (2000), no. 1, 113-182 DOI