Universitat Autònoma de Barcelona
Nonlinear Beltrami equations and quasiconformal flows
It is well understood that every linear Beltrami equation in the plane admits a unique linear family of quasiconformal solutions. It was shown not that long ago that this also works conversely: every linear family of planar quasiconformal homeomorphisms uniquely determines a linear Beltrami equation. In this talk we will analyze a nonlinear counterpart to this correspondence. The talk is based on joint works with K. Astala, D. Faraco, J. Jääskeläinen and L. Székelyhidi.