Growth tightness for groups with contracting elements

Abstract

We establish growth tightness for a class of groups acting geometrically on a geodesic metric space and containing a contracting element. As a consequence, any group with nontrivial Floyd boundary are proven to be growth tight with respect to word metrics. In particular, all non-elementary relatively hyperbolic group are growth tight. This generalizes previous works of Arzhantseva-Lysenok and Sambusetti. Another interesting consequence is that CAT(0) groups with rank-1 elements are growth tight with respect to CAT(0)-metric.

23 pages, 2 figures.More general results are proved.Section 2 from the author's paper arXiv:1205.2994 is transformed in this paper, and will be deleted in that paper. Title changed to reflect these changes

References in corpus (2)

• Patterson-Sullivan measures and growth of relatively hyperbolic groups
• A characterization of higher rank symmetric spaces via bounded cohomology

Cited by in corpus (12)

• Patterson-Sullivan measures and growth of relatively hyperbolic groups
• Growth of quasiconvex subgroups
• Hausdorff dimension of boundaries of relatively hyperbolic groups
• A dynamical characterization of acylindrically hyperbolic groups
• Statistical hyperbolicity of relatively hyperbolic groups
• Marked length spectrum rigidity in groups with contracting elements
• Random walks and contracting elements I: Deviation inequality and Limit laws
• Relative Hyperbolicity of Graphical Small Cancellation Groups
• Large quotients of group actions with a contracting element
• Generic free subgroups and statistical hyperbolicity
• Negligibility of parabolic elements in relatively hyperbolic groups
• Non-elementary convergence groups are acylindrically hyperbolic