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Geometriae Dedicata

, Volume 136, Issue 1, pp 203–220 | Cite as

Quantitative property A, Poincaré inequalities, L p -compression and L p -distortion for metric measure spaces

  • Romain TesseraEmail author
Original Paper

Abstract

We introduce a quantitative version of Property A in order to estimate the L p -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 L p -distortion 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.

Keywords

Uniform embeddings of metric spaces into Banach spaces Property A Poincare inequalities Hilbert compression Hilbert distortion 

Mathematics Subject Classification (2000)

51F99 43A85 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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