Liouville property and regularity of a Hessian quotient equation

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Hessian equations with Infinite Dirichlet Boundary Value (2006, background): “See, for example, [2, 5, 6, 16, 18] for Hessian in Ω and [1, 8, 9, 10] for Hessian on the sphere.”
A Bernstein problem for special Lagrangian equations (2002, background): “the additional assumption that u grows linearly at ∞ and arctanλ 1 +···+arctanλ n = kπ. For c = kπ, the special Lagrangian equation (1.1) in R3 also takes the form (1.2) △u = detD2u. It was proved in [BCGJ] that any strictly convex solution to (1.2) in R3 with quadratic growth at ∞ must be quadratic”