A note on the Dirichlet problem at infinity for manifolds of negative curvature

Abstract

M. T. Anderson and D. Sullivan showed that the Dirichlet problem at infinity for simply connected manifolds is solvable if the curvature satisfies − a 2 > K > − b 2 - {a^2} > K > - {b^2} . Using M. T. Anderson’s method we generalize this statement to manifolds satisfying the weaker bounds − g ( r ) > K > − b 2 - g(r) > K > - {b^2} , where g ( r ) ≈ e λ r g(r) \approx {e^{\lambda r}} , with λ > 1 / 3 \lambda > 1/3 .