DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, January 9, 2002 Padelford C-36 3:45–4:45 pm

Quasiconformal geometry in metric spaces

Bruce Kleiner (University of Michigan)

Quasiconformal homeomorphisms—a class of homeomorphisms generalizing conformal diffeomorphisms—have served as a powerful tool in Teichmüller theory, complex dynamics, the theory of Kleinian groups, and in rigidity theorems like Mostow rigidity. In fact, the definition makes sense in the setting of metric spaces, and it has now become clear that a suitable extension of the classical theory to more general metric spaces would have important applications to the theory of negatively curved manifolds, and to Thurston’s hyperbolization conjecture for 3-manifolds. In the lecture I will explain the background material, and discuss recent joint work with Mario Bonk.

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, https://www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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