Trees and Markov convexity

Details Trees and Markov convexity Trees and Markov convexity

2007-06-04

arxiv.org/abs/0706.0545v1

Mathematics

Metric Geometry

Scientific paper

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.

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