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We consider smooth radial solutions to the Hamiltonian stationary equationwhich are defined away from the origin. We show that in dimension two allradial solutions on unbounded domains must be special Lagrangian. In contrast,for all higher dimensions there exist non-special Lagrangian radial solutionsover unbounded domains; moreover, near the origin, the gradient graph of such asolution is continuous if and only if the graph is special Lagrangian.

Radial solutions of a fourth order Hamiltonian stationary equation