Symmetry properties of viscosity solutions to nonlinear uniformly elliptic equations

\begin{abstract}We study uniformly elliptic fully nonlinear equations $$ F(D^2u, Du, u, x)=0, $$ and prove results of Gidas-Ni-Nirenberg type for positive viscosity solutions of such equations. We show that symmetries of the equation and the domain are reflected by the solution, both in bounded and unbounded domains