Symmetry of viscosity solutions for fully nonlinear parabolic equations

In this paper, we study the symmetry of viscosity solutions for fully nonlinear parabolic equations −ut+F(x,t,u,Du,D2u)=0−ut+F(x,t,u,Du,D2u)=0. We first establish the maximum principles of viscosity solutions for linear parabolic equations. Then the symmetry and monotonicity results of viscosity solutions for fully nonlinear parabolic equations in a bounded domain and a punctured cylinder are proved.