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Tangent bundles of hyperbolic spaces and proper affine actions on $L^p$ spaces (1901.07462v2)
Published 22 Jan 2019 in math.GR and math.MG
Abstract: We define the notion of a negatively curved tangent bundle of a metric measured space. We prove that, when a group $G$ acts on a metric measured space $X$ with a negatively curved tangent bundle, then $G$ acts on some $Lp$ space, and that this action is proper under suitable assumptions. We then check that this result applies to the case when $X$ is a hyperbolic space.