Quasiconformal almost parametrizations of metric surfaces

For zoom details contact Stephan Stadler (stadler@mpim...)

We consider the uniformization problem for 2-dimensional metric surfaces of locally finite Hausdorff measure. By only assuming that a surface is locally geodesic and has finite boundary length, we show that it admits a quasiconformal almost parametrization. In particular, this generalizes the uniformization results of Bonk and Kleiner as well as Rajala. The proof makes use of the theory of energy and area minimizing Sobolev discs developed by Lytchak and Wenger. A large part of this talk is devoted to the existence of Sobolev discs spanning a given Jordan curve in our setting. Based on joint work with Stefan Wenger.