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Durand-Cartagena, Estibalitz ; Jaramillo Aguado, Jesús Ángel ; Shanmugalingam, Nageswari | Centre de Recerca Matemàtica | 2009-10We 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 equivale[...]texto impreso
Durand-Cartagena, Estibalitz ; Jaramillo Aguado, Jesús Ángel ; Shanmugalingam, Nageswari | Universitat Aut?noma de Barcelona | 2016We prove that a locally complete metric space endowed with a doubling measure satisfies an infinity-Poincare inequality if and only if given a null set, every two points can be joined by a quasiconvex curve which "almost avoids" that set. As an [...]
