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.Comment: 14 pages, the needed isometric inequality now derived from the
literature, rather than proved by hand; other minor typos and errors fixe
