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

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 $\mathbb{R}^2$.

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