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Quasisymmetric and bi-Lipschitz parametrization of metric spaces
Colloquium| Speaker: | Juha Heinonen, University of Michigan |
| Location: | 693 Kerr |
| Start time: | Mon, Nov 18 2002, 4:10PM |
We study the problem when a given metric space is locally or globally equivalent to an open set in some Euclidean space via quasisymmetric or bi-Lipschitz homeomorphisms. This problem appears to be difficult. I will present some examples showing that some natural conditions are not sufficient for such local parametrizations to exist. On the other hand, some positive results are given especially in dimension two where the problem has important bearing on the hyperbolization conjecture for negatively curved three manifolds