Hyperbolic groups admit proper affine isometric actions on lp-spaces

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Poincaré inequalities, embeddings, and wild groups (2010, background): “This is necessary, since it was shown in [Yu05] that any hyperbolic group admits a proper (and hence fixed-point free) isometric action on an Lp(µ) space for p large enough.”
Embeddings of Discrete Groups and the Speed of Random Walks (2007, background): “In [44] Yu proved that for every finitely generated hyperbolic group G there exists a large p > 2 for which αp(G) ≥ (1)p .”
Dehn filling in relatively hyperbolic groups (2006, background): “Applications of Mineyev’s construction are myriad (see, for example, [28, 29, 30, 31, 32, 41]).”
Kazhdan and Haagerup properties from the median viewpoint (2007, background): “By the results of G. Yu [Yu05] all cocompact rank one lattices are a-FLp-menable for p large enough.”
Property (T) and rigidity for actions on Banach spaces (2005, background): “V is called complemented if there is another closed subspace Y V such that V =X Y algebraically and topologically.”