Quasiconformal mappings and a Bernstein type theorem over exterior domains in $$\mathbb {R}^2$$

Abstract

We establish the Hölder estimate and the asymptotic behavior at infinity for K-quasiconformal mappings over exterior domains in \(\mathbb {R}^2\). As a consequence, we prove an exterior Bernstein type theorem for fully nonlinear uniformly elliptic equations of second order in \(\mathbb {R}^2\).