Definition and regularity of quasiconformal mappings in metric spaces

Zoltan Balogh (Bern)

We begin by recalling the main results from the theory of QC mappings in the usual Euclidean setting. We continue with the extension of this theory to the setting of metric-measure spaces due to Juha Heinonen and Pekka Koskela.
Our main objective will be to start from minimal assumptions in the definition of quasiconformality and obtain the best possible Sobolev and Hoelder regularity results. In the last part of the lecture we will focus on a recent result by the lecturer in joint work with P. Koskela and S. Rogovin.