12/1/2006

Mario Bonk
University of Michigan

Quasiconformal flows and Q-curvature

The Jacobian problem for quasiconformal maps asks for a characterization of weights on R^n that are comparable to Jacobian determinants of quasiconformal homeomorphisms. It turns out that this problem is closely related to the question when a metric space is bi-Lipschitz equivalent to R^n. In my talk I will discuss some recent joint work with J. Heinonen and E. Saksman in this area that used the technique of quasiconformal flows. As an application of our results we showed that a conformal deformation of R^4 is bi-Lipschitz equivalent to R^4 if it has sufficiently small Q-curvature. This generalizes a result by J. Fu in dimension 2.