Geometric characterizations of $p$-Poincaré inequalities in the metric setting
Geometric characterizations of $p$-Poincaré inequalities in the metric setting
We prove that a locally complete metric space endowed with a doubling measure satisfies an ∞-Poincaré 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 …