%0 Journal Article
%A Durand-Cartagena, Estibalitz
%A Jaramillo Aguado, Jesús Ángel
%A Shanmugalingam, Nageswari
%T Geometric characterizations of p-Poincaré inequalities in the metric setting
%D 2016
%@ 0214-1493
%U https://hdl.handle.net/20.500.14352/22979
%X 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.
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