Quasiconformal and Sobolev mappings on metric measure spaces

Quasiconformal and Sobolev mappings on metric measure spaces

Xiaodan Zhou, Okinawa Institute of Science and Technology Graduate University

Online Talk 

*Please note the change in time*

Zoom linkhttps://princeton.zoom.us/j/594605776

The equivalence of metric, geometric and analytic definitions of quasiconformal mappings in Euclidean space is a fundamental result in  geometric function theory and has been applied widely in different fields. In metric measure spaces, the relations between different definitions usually require appropriate assumptions on the spaces. It is a question of general interest to find minimal assumptions on the metric spaces and on the mapping to guarantee the metric definition implies the analytic or geometric characterization. In this talk, I will present some recent results we achieved in obtaining the analytic property, in particular, the Sobolev regularity of a metric quasiconformal mapping with relaxed spaces and mapping conditions. Unexpectedly, we can apply this to prove results that are new even in the Euclidean setting.

This is joint work with Panu Lahti (Chinese Academy of Sciences).