Motivation to study families of quasiconformal mappings comes from G-compactness questions. In the research of G-compactness properties of linear Beltrami operators it was discovered that there is a natural one-to-one correspondence between linear families of quasiconformal mappings and solutions to linear Beltrami equations. In this talk we discuss a similar connection for nonlinear families and equations. To define a family associated to Beltrami equation one needs to have a uniqueness of normalized solutions. In the case of linear Beltrami equation a homeomorphic solution is uniquely determined by knowing its values at two distinct points. For a nonlinear Beltrami equation this holds, for instance, if the ellipticity is small enough near the infinity, but not hold in general.
Copyright. All Rights Reserved.