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oai:docta.ucm.es:20.500.14352/229792023-08-28T11:16:10Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Durand-Cartagena, Estibalitz author Jaramillo Aguado, Jesús Ángel author Shanmugalingam, Nageswari author 2016 We 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 application, we characterize doubling measures on R satisfying an infinity-Poincare inequality. For Ahlfors Q-regular spaces, we obtain a characterization of p-Poincare inequality for p > Q in terms of the p-modulus of quasiconvex curves connecting pairs of points in the space. A related characterization is given for the case Q - 1 < p <= Q. 0214-1493 10.5565/PUBLMAT_60116_04 https://hdl.handle.net/20.500.14352/22979 https://ddd.uab.cat/record/144963 https://ddd.uab.cat/ Geometric characterizations of p-Poincaré inequalities in the metric setting