Poincaré Inequalities, Embeddings, and Wild Groups
نویسندگان
چکیده
We present geometric conditions on a metric space (Y, dY ) ensuring that almost surely, any isometric action on Y by Gromov’s expander-based random group has a common fixed point. These geometric conditions involve uniform convexity and the validity of nonlinear Poincaré inequalities, and they are stable under natural operations such as scaling, Gromov-Hausdorff limits, and Cartesian products. We use methods from metric embedding theory to establish the validity of these conditions for a variety of classes of metric spaces, thus establishing new fixed point results for actions of Gromov’s “wild groups”.
منابع مشابه
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