  We prove the symmetry of solutions to overdetermined problems for a class of
fully nonlinear equations, namely Hessian quotient equations and Hessian
quotient curvature equations. Our approach is based on establishing a
Rellich-Pohozaev type identity for Hessian quotient equations and using a P
function. Our result generalizes the overdetermined problems for k-Hessian
equations and k-curvature equations.
