Title:
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Geometric characterizations of p-Poincaré inequalities in the metric setting
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Author:
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Durand-Cartagena, Estibalitz; Jaramillo, Jesús A; Shanmugalingam, Nageswari
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Abstract:
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We prove that a locally complete metric space endowed with a doubling measure satisfies an ∞-Poincar'e 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 ∞-Poincaré inequality. For Ahlfors Q-regular spaces, we obtain a characterization of p-Poincaré 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. |
Subject(s):
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-P-Poincaré inequality -Metric measure space -Thick quasiconvexity -Qua- siconvexity -Singular doubling measures in R -Lip-lip condition |
Rights:
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open access
Tots els drets reservats.
https://rightsstatements.org/vocab/InC/1.0/ |
Document type:
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Article |
Published by:
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Share:
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Uri:
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https://ddd.uab.cat/record/144963
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