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We study expansions near the boundary of solutions to the Dirichlet problemfor minimal graphs in the hyperbolic space and prove the local convergence ofsuch expansions if the boundary is locally analytic. As a consequence, we provea conjecture by F.-H. Lin that the minimal graph is analytic up to the boundaryif the boundary is analytic and the minimal graph is smooth up to the boundary.

The convergence of boundary expansions and the analyticity of minimal surfaces in the hyperbolic space