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Bi-Lipschitz parametrizations of metric spaces and smoothability of topological manifolds
The problem of characterizing metric spaces that are locally bi-Lipschitzly Euclidean has turned out to be a difficult one. Examples due to Edwards, Semmes, Laakso, Bishop, and others show that no simple geometric answer can be expected to this problem. In this talk, I present a characterization for 2-dimensional spaces based on the flat differential forms of Whitney. Moreover, a similar sufficient condition is given in all dimensions. The latter also yields a new criterion for the smoothability of topological manifolds.
Thursday, April 27, 2006, 245 Altgeld Hall, 4:00 p.m.
Mathematics Colloquia homepage