Symmetry of Solutions of Minimal Gradient Graph Equations on Punctured Space

In this paper, we study symmetry and existence of solutions of minimal gradient graph equations on punctured space R \ {0}, which include the Monge-Ampère equation, inverse harmonic Hessian equation and the special Lagrangian equation. This extends the classification results of Monge-Ampère equations. Under some conditions, we also give the characterization of the solvability on exterior Dirichlet problem in terms of their asymptotic behaviors.

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