Boundary Expansions for Constant Mean Curvature Surfaces in the Hyperbolic Space

Abstract

We study expansions near the boundary of solutions to the Dirichlet problem for the constant mean curvature equation in the hyperbolic space. With a characterization of remainders of the expansion by multiple integrals, we establish optimal asymptotic expansions of solutions with boundary values of finite regularity and demonstrate a slight loss of regularity for coefficients.