Boundary regularity of minimal graphs in the hyperbolic space

Abstract

Abstract F.-H. Lin (1989) studied minimal graphs of the Dirichlet problem in the hyperbolic space and proved that any such minimal graph has the same global regularity as the boundary if the dimension of the minimal graph is even and that there is an obstacle to the higher regularity if the dimension is odd. We discuss the odd-dimensional case and study how the higher regularity is obstructed. We introduce the logarithmic distance to the boundary as an additional independent self-variable and establish concise boundary regularity for the minimal graph.