Erratum: On the Dirichlet problem for minimal graphs in hyperbolic space

Abstract

R n × {0} that can be identified with the asymptotic infinity of Hn+1. Let Nn−1 ⊂ Hn+1 ∞ be a closed embedded (n − 1)-dimensional submanifold. Then there exists a complete absolutely area-minimizing integral n-current Σ asymptotic to Nn−1 at infinity; see, for example [1, 2]. It was also noted in [1, 2] that in the case n≤ 6, currents obtained are smoothly embedded complete hypersurfaces. In the case n ≥ 7, as in the Euclidean case, there can be a singular set of Hausdorff dimension at most n− 7.