Publication: Geometric characterizations of p-Poincaré inequalities in the metric setting
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2016
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Universitat Aut�noma de Barcelona
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Abstract
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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En el año 2013 se publicó el preprint en Report nº 15, el Pdf se puede ver en este registro.