In this paper, we prove the symmetry of the solution to overdetermined problem for the equation σₖ(D²u-uI)=Cₙᵏ 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.
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Gao et al. (2022) studied this question.
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