Uniqueness of boundary blowup solutions to kk-curvature equation

We consider the boundary blowup problem for the kk-curvature equation, i.e., Hk[u]=f(u)g(|Du|)Hk[u]=f(u)g(|Du|) in an nn-dimensional domain ΩΩ, with the boundary condition u(x)→∞u(x)→∞ as dist(x,∂Ω)→0. We prove the uniqueness result under some hypotheses.