6533b7d5fe1ef96bd1263eb4

RESEARCH PRODUCT

SPACES OF SMALL METRIC COTYPE

Ellen VeomettKevin Wildrick

subject

Mathematics::Functional AnalysisPure mathematics30L05 46B85010102 general mathematicsBanach spaceMetric Geometry (math.MG)0102 computer and information sciences16. Peace & justice01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional AnalysisMetric spaceMathematics - Metric Geometry010201 computation theory & mathematicsConverseMetric (mathematics)FOS: MathematicsMathematics::Metric GeometryGeometry and Topology0101 mathematicsIsoperimetric inequalityUltrametric spaceAnalysisMathematics

description

Naor and Mendel's metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz equivalent to an ultrametric space has infinimal metric cotype 1. We discuss the invariance of metric cotype inequalities under snowflaking mappings and Gromov-Hausdorff limits, and use these facts to establish a partial converse of the main result.

yearjournalcountryeditionlanguage
2010-01-19Journal of Topology and Analysis
https://doi.org/10.1142/s1793525310000422