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BIRS Workshop Lecture Videos

Quasisymmetric vs Bi-Lipschitz maps Dymarz, Tullia


On a metric space, there are various classes of functions which respect aspects of the metric space structure. One of the most basic classes is the bi-Lipschitz maps Another possibly much larger class con- sists of the so-called quasisymmetric maps. On both Euclidean space and the p-adics, there are many quasisymmetric maps which are not bi- Lipschitz. However, on the product of Euclidean space with the p-adics, we show that all quasisymmetric maps are bi-Lipschitz. Furthermore,\\r\\n3 our proof does not use any direct analysis but instead uses results on quasi-isometries and spaces of negative curvature.

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