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

Borbély, Albert

doi:10.1090/S0002-9939-1992-1069289-8

A note on the Dirichlet problem at infinity for manifolds of negative curvature
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by Albert Borbély PDF

Proc. Amer. Math. Soc. 114 (1992), 865-872 Request permission

Abstract:

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

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