Seminar by Maxime Fortier Bourque (University of Toronto)

Title: Extremal quasiconformal embeddings

2015.06.29 | Christine Dilling

Date Wed 15 Jul
Time 15:15 16:15
Location Aud D3


I will talk about a theorem of M.S. Ioffe which characterizes quasiconformal embeddings between Riemann surfaces that have minimal dilatation in their homotopy class. These extremal embeddings are obtained by stretching horizontally with respect to a pair of quadratic differentials. Ioffe's theorem can be used to prove Strebel's theorem on quadratic differentials with closed trajectories, to give a criterion for when one Riemann surface embeds conformally inside another, or to show that if two conformal embeddings are homotopic then they are homotopic through conformal embeddings.