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In this paper, we are concerned with the monotonic and symmetric properties of convex solutions Monge-Amp\`ere systems for instance, considering equation* (D²uⁱ) =fⁱ (x, u, uⁱ), \ 1 i m, equation* over unbounded domains of various cases, including the whole spaces Rⁿ, the half spaces Rⁿ_+ and the unbounded tube shape domains in Rⁿ. We obtain monotonic and symmetric properties of the solutions to the problem with respect to the geometry of domains and the monotonic and symmetric properties of right-hand side terms. The proof is based on carefully using the moving plane method together with various maximum principles and Hopf's lemmas.
Zhang et al. (Mon,) studied this question.