Spaces of small metric cotype

Details Spaces of small metric cotype Spaces of small metric cotype

2010-01-19

arxiv.org/abs/1001.3326v3

Mathematics

Metric Geometry

14 pages, the needed isometric inequality now derived from the literature, rather than proved by hand; other minor typos and e

Scientific paper

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.

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