The exterior Dirichlet problem for special Lagrangian equations in dimensions n≤4

In this paper, we establish the existence theorem for the exterior Dirichlet problem for special Lagrangian equations with prescribed asymptotic behavior at infinity. This extends the previous results on Monge-Ampère equations and Hessian equations to special Lagrangian equations in dimensions n≤4, which is from calibrated geometry. More generally, we prove that the result is also true for Hessian quotient equations with 0≤l