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Michel Coornaert 《Geometriae Dedicata》2002,95(1):59-64
It is known that in a word hyperbolic group the stable exponent of every nontorsion element is an integer. We prove that this is also true in finitely generated nilpotent groups. On the other hand, we show that for any rational number 1 there exists a torsionfree CAT(0) group containing an element whose stable exponent is equal to . 相似文献
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Michel Coornaert Athanase Papadopoulos 《Transactions of the American Mathematical Society》1999,351(7):2745-2762
Let be a -space which is spherically symmetric around some point and whose boundary has finite positive dimensional Hausdorff measure. Let be a conformal density of dimension on . We prove that is a weak limit of measures supported on spheres centered at . These measures are expressed in terms of the total mass function of and of the dimensional spherical function on . In particular, this result proves that is entirely determined by its dimension and its total mass function. The results of this paper apply in particular for symmetric spaces of rank one and semi-homogeneous trees.
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Let V be a finite-dimensional vector space over a field
and let G be a sofic group. We show that every injective linear cellular automaton τ: V
G
→ V
G
is surjective. As an application, we obtain a new proof of the stable finiteness of group rings of sofic groups, a result
previously established by G. Elek and A. Szabó using different methods. 相似文献
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In this paper, we study some asymptotic aspects of the positiveeigenfunctions of the combinatorial Laplacian associated toa homogeneous tree. The results are inspired by results of DennisSullivan concerning -harmonic functions on the hyperbolic spacesHn and contained in the paper [9]. 相似文献
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Tullio Ceccherini-Silberstein Michel Coornaert Fabrice Krieger 《Journal d'Analyse Mathématique》2014,124(1):59-81
We prove an analogue of Fekete’s lemma for subadditive right-subinvariant functions defined on the finite subsets of a cancellative left-amenable semigroup. This extends results previously obtained in the case of amenable groups by E. Lindenstrauss and B. Weiss and by M. Gromov. 相似文献
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Let M be a semisimple left module of finite length over a ring R and let G be an amenable group. We show that an R-linear cellular automaton τ:MG → MG is surjective if and only if it is pre-injective. 相似文献
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Let G be an amenable group and let A be a finite set. We prove that if X ? A G is a strongly irreducible subshift then X has the Myhill property, that is, every pre-injective cellular automaton ?? : X ?? X is surjective. 相似文献
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Let Γ be a word hyperbolic group M. Gromov has constructed a compact space equipped with a flow which is defined up to orbit-equivalence and which is called the geodesic flow of Γ. In the special
case where Γ is the fundamental group of a Riemannian manifold of negative sectional curvature, is the unit tangent bundle of the manifold equipped with the usual geodesic flow. In this paper, we construct, for every
hyperbolic group Γ, a subshift of finite type and a continuous map from the suspension of this subshift onto , which is uniformly bounded-to-one and which sends each orbit of the suspension flow onto an orbit of the geodesic flow.
Received: 25 January 2002 / Revised version: 20 August 2002
Mathematics Subject Classification (2000): 20F67, 20F65, 20F69, 53C23, 53C21, 37D40, 37B10, 54H20 相似文献