2026-08-20T15:37:15Zhttps://docta.ucm.es/rest/oai/request

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

Geometric characterizations of p-Poincaré inequalities in the metric setting Durand-Cartagena, Estibalitz Jaramillo Aguado, Jesús Ángel Shanmugalingam, Nageswari 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. 2023-06-18T05:40:31Z 2023-06-18T05:40:31Z 2023-06-18T05:40:31Z 2016 journal article https://hdl.handle.net/20.500.14352/22979 0214-1493 10.5565/PUBLMAT_60116_04 spa DMS-1200915 MTM2012-34341 restricted access Universitat Aut�noma de Barcelona