Asymptotic behaviour of harmonic functions in negative curvature (Q1906919)

Summary: Let \(M\) be a complete simply connected Riemannian manifold whose sectional curvatures are bounded between two negative constants. It is shown that, for a given harmonic function on \(M\), non-tangential properties of convergence, boundedness and finiteness of energy are equivalent for almost every point of the geometric boundary. This is a ``geometric'' analogue of Calderón-Stein theorem in the Euclidean half-space. The proof is using Brownian motion, like J. Brossard's one for the Euclidean case.