标题： 可解双曲群 显示英文标题

标题： Amenable hyperbolic groups

摘要： 我们给出了非初等Gromov双曲且可换的局部紧群的完整特征。它们与离散或连续一参数紧化自同构群的映射环面类相同。此外，我们还描述了所有具有共紧可换子群的Gromov双曲局部紧群：模去一个紧正规子群，这些群要么是秩一简单李群，要么是作用在端点集上双重传递的半正则树的自同构群。作为应用，我们证明了具有尖点均匀非均匀格的双曲局部紧群类非常有限。 显示英文摘要

摘要： We give a complete characterization of the locally compact groups that are non-elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semi-regular trees acting doubly transitively on the set of ends. As an application, we show that the class of hyperbolic locally compact groups with a cusp-uniform non-uniform lattice, is very restricted.