Quantitative property A , Poincaré inequalities , L p - compression and L p - distortion for metric measure spaces . Romain Tessera
نویسنده
چکیده
We introduce a quantitative version of Property A in order to estimate the Lp-compressions of a metric measure space X. We obtain various estimates for spaces with sub-exponential volume growth. This quantitative property A also appears to be useful to yield upper bounds on the Lpdistortion of finite metric spaces. Namely, we obtain new optimal results for finite subsets of homogeneous Riemannian manifolds. We also introduce a general form of Poincaré inequalities that provide constraints on compressions, and lower bounds on distortion. These inequalities are used to prove the optimality of some of our results. Mathematics Subject Classification: Primary 51F99; Secondary 43A85.
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تاریخ انتشار 2008