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- W4643159 abstract "We study a geometric characterization of ∞−Poincare inequality. We show that a path-connected complete doubling metric measure space supports an ∞−Poincare inequality if and only if it is thick quasi-convex. We also prove that these two equivalent properties are also equivalent to the purely analytic property that N1,∞(X) = LIP∞(X), where LIP∞(X) is the collection of bounded Lipschitz functions on X and N1,∞(X) is the Newton-Sobolev space studied in [DJ]." @default.
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- W4643159 date "2009-10-01" @default.
- W4643159 modified "2023-09-24" @default.
- W4643159 title "Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞" @default.
- W4643159 hasPublicationYear "2009" @default.
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