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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 |
Description
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