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oai:docta.ucm.es:20.500.14352/444662023-08-28T13:27:34Zcom_20.500.14352_14col_20.500.14352_15

Durand-Cartagena, Estibalitz Jaramillo Aguado, Jesús Ángel Shanmugalingam, Nageswari 2023-06-20T03:48:05Z 2023-06-20T03:48:05Z 2009-10 https://hdl.handle.net/20.500.14352/44466 http://www.recercat.cat/bitstream/handle/2072/47933/Pr895.pdf?sequence=1 http://www.crm.cat/en/Pages/default.aspx 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]. eng open access Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞ journal article