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

Abstract

We establish the H\"{o}lder 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 $\mathbb{R}^2$.