Zoltán Balogh (Universität Bern): Stability of extremal quasiconformal maps

Extremal quasiconforml maps are minimisers of the quasiconformal distortion and thus they are as close as possible to conformal maps. In this talk we consider two classical examples: the linear stretch and the radial spiral-stretch map and study their quantitative stability. We prove that if the quasiconformal distortion of a map is close to be minimal then the map must be close to the minimiser. This is a joint work (still in progress) with Károly Böröczky.