(untitled) (Journal of Partial Differential Equations, 2023)
In this paper, we prove the symmetry of the solution to overdetermined problem for the equation σ_k(D^2u-uI)=C_n^k in hyperbolic space. Our approach is based on establishing a Rellich-Pohozaev type identity and using a P function. Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.