Trees and Markov Convexity
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We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion. We also introduce a new metric invariant called Markov convexity, and show how it can be used to compute the Euclidean distortion of any metric tree up to universal factors.
AMS Mathematics Subject Classification:51F99 05C12 05C05 60B99
Keywords and phrases:Metric trees bi-Lipschitz embeddings uniform convexity
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