Durand-Cartagena, EstibalitzJaramillo Aguado, Jesús ÁngelShanmugalingam, Nageswari2023-06-182023-06-1820160214-149310.5565/PUBLMAT_60116_04https://hdl.handle.net/20.500.14352/22979En el año 2013 se publicó el preprint en Report nº 15, el Pdf se puede ver en este registro.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.spajournal articlehttps://ddd.uab.cat/record/144963https://ddd.uab.cat/restricted access517.98p-Poincare inequalitymetric measure spacethick quasiconvexityquasiconvexitysingular doubling measures in RLip-lip conditionAnálisis funcional y teoría de operadores