%0 Journal Article
%A Durand-Cartagena, Estibalitz
%A Jaramillo Aguado, Jesús Ángel
%A Shanmugalingam, Nageswari
%T Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞
%D 2009
%U https://hdl.handle.net/20.500.14352/44466
%X We study a geometric characterization of ∞−Poincaré inequality. We show that a path-connected complete doubling metric measure space supports an ∞−Poincaré inequality if and only if it is thick quasi-convex. We also prove that these two equivalent properties are also equivalent to the purely analytic property that N1,∞(X) = LIP∞(X), where LIP∞(X) is the collection of bounded Lipschitz functions on X and N1,∞(X) is the Newton-Sobolev space studied in [DJ].
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