Seminars & Colloquia Calendar

Abstract: The concept of “quasiconformal motion” was first introduced by Sullivan and Thurston. They asserted that any quasiconformal motion of a set in the sphere over an interval can be extended to the sphere. However, in our recent work, we gave a counterexample to that assertion. Based on this counterexample, we introduced a new concept called “tame quasiconformal motion” and show that their assertion is true for tame quasiconformal motions. Actually, we proved a much more general result that, any tame quasiconformal motion of a closed set in the sphere, over a simply connected Hausdorff space, can be extended as a quasiconformal motion of the sphere. Furthermore, we showed that this extension can be done in a conformally natural way. The fundamental idea is to show that the Teichmuller space of a closed set in the sphere is a “universal parameter space” for tame quasiconformal motions of that set over a simply connected Hausdorff space.

This talk is based on a joint work with Sudeb Mitra, Hiroshige Shiga, and Zhe Wang.