Poincaré inequalities, embeddings, and wild groups

Poincaré inequalities, embeddings, and wild groups

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 st...

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Veröffentlicht in:Compositio mathematica 2011-09, Vol.147 (5), p.1546-1572
Hauptverfasser: Naor, Assaf, Silberman, Lior
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Sprache:eng
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Cartesian
Convexity
Inequalities
Metric space
Nonlinearity
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Silberman, Lior
description 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’.
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source EZB-FREE-00999 freely available EZB journals; Cambridge University Press Journals Complete
subjects Cartesian
Convexity
Inequalities
Metric space
Nonlinearity
title Poincaré inequalities, embeddings, and wild groups
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